Baumdiagramm: Ziehen ohne Zurücklegen

In diesem Artikel erkläre ich dir, wie du ein Baumdiagramm für „Ziehen ohne Zurücklegen“ erstellst. Hierbei klären wir zunächst, was „Ziehen ohne Zurücklegen“ überhaupt bedeutet, dann zeige ich dir an einem Beispiel, wie du für diesen Sachverhalt ein Baumdiagramm erstellst. Als letztes gehe ich nochmals auf die beiden Rechenregeln, die es an einem Baumdiagramm gibt, also die „Pfadmultiplikation“ und die „Summenregel“ ein, indem ich sie bei einem Beispiel anwende.

Was du vorher wissen solltest:

Ziehen ohne Zurücklegen:

Im letzten Artikel habe ich dir ja schon erklärt, was „Ziehen mit Zurücklegen“ bedeutet. „Ziehen ohne Zurücklegen“ möchte ich dir auch wieder an einer Urne in der rote und blaue Kugeln enthalten sind, erklären. „Ziehen ohne Zurücklegen“ heißt eigenlich nur, dass eine Kugel, die einmal aus einer Urne entnommen wurde, nicht wieder zurückgelegt wird. Oder aber, etwas allgemeiner ausgedrückt, dass nie wieder die Ausgangssituation hergestellt wird und dass sich von Stufe zu Stufe die Wahrscheinlichkeiten ändern. Warum ist das so? Schauen wir uns hierzu diese Urne an:

Urne mit Kugeln

Wie du siehst  beinhaltet diese Urne 3 rote und 2 blaue Kugeln. Insgesamt sind als 5 Kugeln vorhanden. Wenn wir jetzt zum Beispiel eine rote Kugel ziehen, dann hat diese rote Kugel die relative Häufigkeit von [latex size=25]\frac {3}{5}[/latex], da 3 von 5 Kugeln rot sind.

Urne mit Kugeln

Diese Kugel legen wir nun nicht mehr in die Urne zurück, also sind in dieser Urne nun 2 rote und 2 blaue Kugeln (eine rote fehlt). Jetzt haben die möglichen Ausgänge also andere Wahrscheinlichkeiten. Zum einen hat sich die Gesamtzahl verringert, zum anderen die Anzahl an roten Kugeln. Die nächste rote Kugel hat also nicht mehr die Wahrscheinlichkeit [latex size=25]\frac {3}{5}[/latex], sondern [latex size=25]\frac {2}{4}[/latex] (gekürzt [latex size=25]\frac {1}{2}[/latex]), da nun 2 von 4 Kugeln rot sind.

Der große Unterschied zum „Ziehen mit Zurücklegen“ ist also, dass nicht mehr jede Stufe eines Experimentes die selbe Wahrscheinlichkeit hat. Hier ändern sich die Wahrscheinlichkeiten von Zug zu Zug.

Urne mit Kugeln

Erstellung eines Baumdiagramms:

Die Erstellung eines Baumdiagramms möchte ich dir nun anhand dieser Urne erklären.

Aus dieser Urne ziehen wir nun eine Kugel, legen die erste Kugel aber nicht zurück in die Urne. Wir erstellen somit ein Baumdiagramm für „Ziehen mit Zurücklegen“:

1. Als erstes überlegen wir uns wieviele verschiedene Möglichkeiten dieser Zug hat! In diesem Fall sicherlich zwei, denn wir können eine rote oder eine blaue Kugel ziehen. Das heißt, dass wir nun zwei Abzweigungen brauchen (allgemein: eben genau gleich viele Abzweigungen wie Möglichkeiten).

Erstellung Baumdiagramm

Wie du siehst besteht bei diesem Vorgehen noch gar kein Unterschied zu „Ziehen mit Zurücklegen“.

2. Nachdem wir nun die Anzahl der Abzweigungen ermittelt haben, werden die Enden dementsprechend beschriftet. Eine Abzweigung steht für den Ausgang rot, die Andere für blau.

Erstellung Baumdiagramm

Alternativ zu zwei farbigen Punkten, kannst du bei dieser Situation auch wieder gerne mit einem r und einem b beschriften.

Auch hier ist noch kein Unterschied zu „Ziehen mit Zurücklegen“.

3. Nun werden die relativen Häufigkeiten an die Seite der jeweiligen Äste hingeschrieben.

Erstellung Baumdiagramm

In diesem Fall hat die rote Kugel die relative Häufigkeit [latex size=25]\frac {3}{5}[/latex], da drei von fünf Kugeln rot sind und die blaue Kugel [latex size=25]\frac {2}{5}[/latex], da zwei von fünf Kugeln blau sind.

Die erste von zwei Ziehungen ist nun beendet und wir sind genau wie bei „Ziehen mit Zurücklegen“ vorgegangen. Nun starten wir mit der zweiten Ziehung und hier fängt der unterschiedliche Ansatz zu „Ziehen mit Zurücklegen“ an, denn nun stellen wir nicht wieder die Ausgangsituation her!

Was sich allerdings nicht ändert, ist, dass wir immernoch jeweils eine rote oder eine blaue Kugel ziehen können, ganz unabhängig davon was als erstes gezogen wurde. Also ergänzen wir dieses Baumdiagramm mit jeweils zwei Ästen, die wir wieder mit rot und blau beschriften!

Bei den relativen Häufigkeiten musst du nun aufpassen, denn sie unterscheiden sich nicht nur von den Wahrscheinlichkeiten der ersten Stufe, sie unterscheiden sich auch bei beiden Abzweigungen bei der zweiten Stufe.

Erstellung Baumdiagramm

Die linke Seite steht dafür, dass im Vorfeld eine rote Kugel gezogen wurde, das heißt, dass nun 2 von 4 Kugeln rot sind und 2 von 4 blau. Also ist die relative Häufigkeit sowohl von rot als auch von blau [latex size=25]\frac {2}{4}[/latex] bzw. gekürzt [latex size=25]\frac {1}{2}[/latex] (wobei ich an einem Baumdiagramm zunächst nicht kürze).

Erstellung Baumdiagramm

Auf der rechten Seite haben wir auf der ersten Stufe eine blaue Kugel entnommen. Das heißt, dass wir auch hier wieder 4 Kugeln insgesamt haben, allerdings sind davon drei rot und nur eine blau. Also ist hier die relative Häufigkeit von rot [latex size=25]\frac {3}{4}[/latex] und von blau [latex size=25]\frac {1}{4}[/latex].

Erstellung Baumdiagramm Ziehen ohne Zurücklegen

Dies ist nun das vollständig ausgefüllte Baumdiagramm! Wie du siehst fängt der Unterschied zwischen „Ziehen mit Zurücklegen“ und „Ziehen ohne Zurücklegen“ auf der zweiten Stufe bzw. beim zweiten Zug an.

Unterschied Baumdiagramm für Ziehen mit und ohne Zurücklegen

Rechenbeispiele an diesem Baumdiagramm:

Beispiel 1: Gesucht ist die Wahrscheinlichkeit von zwei roten Kugeln

Summenregel

P(r,r) = P(Summenregel,Pfadmultiplikationsregel) = [latex size=30]\frac {3}{5}[/latex] x [latex size=30]\frac {2}{4}[/latex] = [latex size=30]\frac {6}{20}[/latex] = [latex size=30]\frac {3}{10}[/latex]

Endwahrscheinlichkeiten werden, wie ich dir schon im letzten Artikel erklärt habe, mit der Pfadmultiplikationsregel ermittelt.

Beispiel 2: Gesucht ist die Wahrscheinlichkeit von einer blauen Kugel

Wie du siehst handelt es sich um zwei verschiedene Äste von denen wir nun die Endwahrscheinlichkeiten jeweils mit der Produktregel berechnen und diese dann mithilfe der Summenregel addieren. Die Formulierung „eine blaue Kugel“ sagt ja keinesfalls aus, dass diese Kugel als erstes gezogen werden muss. Diese blaue Kugel kann offensichtlich als erstes oder als zweites gezogen werden, sodass es genau diese beiden Äste sind, von denen wir die Wahrscheinlichkeit ermitteln müssen:

P(r,b) = P(,) = [latex size=30]\frac {3}{5}[/latex] x [latex size=30]\frac {2}{4}[/latex] = [latex size=30]\frac {6}{20}[/latex] = [latex size=30]\frac {3}{10}[/latex]

P(b,r) = P(,) = [latex size=30]\frac {2}{5}[/latex] x [latex size=30]\frac {3}{4}[/latex] = [latex size=30]\frac {6}{20}[/latex] = [latex size=30]\frac {3}{10}[/latex]

P(,) + P(,) = [latex size=30]\frac {3}{10}[/latex] + [latex size=30]\frac {3}{10}[/latex] = [latex size=30]\frac {6}{10}[/latex] = [latex size=30]\frac {3}{5}[/latex]

 

Einen kleinen Tipp habe ich noch:

Beim „Ziehen ohne Zurücklegen“ ändert sich die Gesamtzahl von Stufe zu Stufe um eins. Das heißt, dass, wenn auf der ersten Stufe 5 Kugeln vorhanden waren, dann sind es auf der zweiten Stufe 4. Wenn wir sogar ein drittes Mal ziehen würden, dann wären es dort 3. Beim 4. Zug dann zwei und beim 5. Zug dann eine Kugel. Mir persönlich hilf es immer so zu starten, dass ich als erstes ein unausgefülltes Baumdiagramm zeichne, dann auf jeder Stufe die Gesamtheit unter dem Bruch eintrage (das ist übrigens der Grund warum sich Brüche zur Beschriftung besser eignen als Dezimalzahlen).

Das sieht dann erst so aus:

Tipp Baumdiagramm

Erst als letztes kümmere ich mich um die Zähler der jeweiligen Brüche, indem ich mir stets die Frage stelle, wieviele Kugeln (hier zumindest Kugeln) der jeweiligen Farbe noch vorhanden sind!

Auf YouTube ansehen: >>>Hier klicken<<<

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  144. L’UFCM a constaté depuis quelques mois l’accroissement des tromperies à la « roqya ». Les témoignages de personnes victimes de ces pratiques se multiplient et présentent les mêmes caractéristiques : « Une personne vous appelle et vous propose une séance de « roqya » gratuite. Cette personne vous propose de rappeler un numéro prétendu gratuit, souvent un numéro commençant par 0 800… » Mais, dans les faits, cette prestation est loin d’être gratuite, puisque la conversation est facturée à vos frais et à votre insu. Au-delà de l’aspect juridique qui est traité à ce jour par le pôle juridique de l’UFCM[1], ce procédé soulève la problématique de sa conformité au Coran et à la Sunna. En effet, la « roqya » peut se définir comme une thérapie qui permet de soigner les actes de sorcellerie, de mauvais œil et également de se protéger contre ces derniers. Par conséquent, est-il possible de la pratiquer par téléphone et quelles sont les exigences édictées par le Coran et la Sunna ? 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Ainsi, pour se prémunir des maux liés au mauvais œil ou à la sorcellerie, il convient régulièrement de lire le Coran et faire des invocations notamment celles du matin et du coucher, de réciter régulièrement la sourate « La vache », de renouveler son intention, de placer la certitude dans son cœur, d’effectuer ses prières etc., et surtout de demander à Allah la meilleure des protections. Toutefois, dans certaines conditions, il est nécessaire de recourir à un soignant. C’est à ce stade qu’il convient d’être vigilant. Il ne suffit pas de se rendre auprès d’une personne qui se présente avec la qualité de cheikh ou d’imam pour accepter de lui confier cette pratique. Comme pour tout procédé et encore plus lorsque cela relève de considérations religieuses, il est important de bien choisir son soignant car ce dernier est tenu de posséder des qualités bien affirmées. La maîtrise du Coran et des traditions prophétiques en la matière est une condition sine qua none, mais insuffisante. La personne doit également avoir des notions de psychologie afin de déterminer la part de sorcellerie et celle de troubles psychologiques fréquents chez les patients. La personne doit posséder une bonne hygiène de vie, notamment spirituelle puisqu’il n’est pas inutile de rappeler que le succès de la « roqya » dépend de Dieu. Ces critères sont difficilement évaluables, surtout par une personne qui est affectée par un mal-être, quelle que soit sa source. C’est pourquoi les proches doivent accompagner la personne dans la recherche d’un soignant qualifié et reconnu comme tel par des référents religieux de la localité (imam, responsables associatifs, etc.). De manière générale, le soignant doit posséder des qualités déterminées que nous pouvons synthétiser de la manière suivante. Il doit : être en capacité de lire le Coran, croire avec certitude au Coran, être empreint de piété, connaître les pièges et les caractéristiques du diable et des djinns, connaître la méthode prophétique de la « roqya », disposer de connaissances de base en psychologie, avoir la conviction que le succès de sa thérapie dépend de Dieu. A l’exception de la première exigence, il semble difficile de vérifier les autres conditions dans le cadre d’un entretien téléphonique avec une personne que nous n’avons jamais rencontrée, même si elle se présente sous le titre de « cheikh » ou d’un imam. Par conséquent, ces conditions soulignent une première limite quant au recours à la « roqya » par téléphone. Par ailleurs, à l’instar de tout médecin, le soignant doit, avant de prodiguer des conseils ou une médication, procéder à une consultation. Ainsi, un environnement adéquat est indispensable pour la réalisation d’une « roqya ». Il est enfin inconcevable qu’un médecin puisse vous affirmer par téléphone connaître votre maladie et attester pouvoir vous guérir. Vous auriez plus que des doutes sur ce prétendu médecin. II- Un environnement propice et la réalisation d’une consultation préalable à la réalisation d’une « roqya » Il est intéressant de noter que, dans son ouvrage « Comment se protéger des djinns & satan », Wahîd ‘Abdussalâm Bâli évoque l’importance du climat pour réaliser une roqya[2]. Ainsi, il expose les points suivants : « 1. Préparer le climat adéquat en faisant par exemple sortir les images et les statues de la pièce où on va soigner le malade, pour permettre aux anges d’y entrer. 2. Débarrasser le sujet de tout ce qu’il peut porter sur lui comme talismans ou amulettes et les brûler. 3. Éteindre tout ce qui peut émettre le son de la musique et des chants. 4. Vider le lieu de tout ce qui comporte une infraction à la shari‘a à savoir, par exemple, la présence d’un homme qui porte de l’or ou une femme qui ne porte pas le voile légal – al-hijab. 5. Donner au malade et à sa famille une leçon de dogme de façon à ce que leurs cœurs ne soient pas attachés à un autre qu’Allah. 6. Leur faire savoir que la façon de soigner est différente de celle des sorciers et des charlatans et que le Coran recèle guérison et miséricorde, comme l’a informé Allah le Puissant et le Majestueux. 7. Diagnostiquer son cas : pour cela poser des questions au malade pour s’assurer de la présence de tous les symptômes (…) ». Or, dans les témoignages communiqués, l’interlocuteur qui se présente comme soignant ne pose aucune question aux personnes. Il débute ainsi la « roqya » directement par une récitation du Coran. En outre, il est intéressant de souligner que dans l’un des témoignages communiqués à l’UFCM, l’interlocuteur demandait à la personne de remplir successivement des verres de lait, d’huile, d’eau etc. et de les poser par la suite sur la table de la salle à manger. Au point que la personne s’est retrouvée avec une multitude de verres posés sur la table. Le comble est que la personne ignorait ce qu’elle devait en faire lorsqu’elle a pris conscience de la tromperie. Nous constatons par conséquent qu’une « roqya » ne peut être réalisée dans un environnement quelconque. En effet, une procédure de diagnostic est essentielle. Nous pouvons à titre d’exemple faire le parallèle avec un rendez-vous chez le médecin ; ce dernier ne peut vous prescrire une ordonnance sans au préalable vous avoir ausculté et interrogé sur les différents symptômes que vous ressentez physiquement. A défaut, au lieu de guérir vous allez aggraver vos maux. Cette attitude vigilante du médecin traitant doit se retrouver lorsque nous envisageons le recours à une « roqya ». Pour illustrer ce propos, nous citerons l’exemple de l’anthropologue, spécialiste de l’islam européen, Farid El Asri, chercheur associé au Centre Jacques Berque, qui nous rapporte une situation alarmante suite à une « roqya » : « Une jeune femme en Belgique (…) est morte suite à une tentative d’exorcisme. Pendant les séances, les fkihs (imams) utilisent normalement de l’eau « coranisée ». Pour cette jeune femme, prétendument stérile, les exorcistes ont carrément plongé son visage dans l’eau et quand elle tentait d’en sortir pour respirer, les guérisseurs estimaient qu’il s’agissait du jinn qui l’habitait et ils replongeaient son visage dans l’eau. Pendant le procès, la famille de la défunte s’est présentée comme musulmane et a accusé ces pratiques d’être extérieures à l’islam quand les guérisseurs estimaient qu’ils avaient simplement fait ce qu’ils pouvaient. Le fait de recourir trop systématiquement au fkih risque également de faire passer une crise d’épilepsie, par exemple, pour une crise de possession. »[3] Nous allons aborder enfin la dernière problématique, celle relative aux honoraires du soignant. III- Les honoraires du soignant Le Prophète, bénédictions et salut sur lui, « a agréé les Compagnons qui ont été payés pour la roqya ». Il est dès lors autorisé de rémunérer un soignant en contrepartie d’une prestation. Toutefois, cette rémunération doit être raisonnable et surtout clairement définie avant le traitement. En outre, nous ne pouvons que souligner et rappeler que, si la roqya est réalisée dans un cadre sérieux, il convient de procéder à toutes les déclarations administratives. Comme pour tout contrat, vous devez exiger un document écrit et le praticien doit préciser quels sont ses engagements exacts afin d’éviter tout litige postérieur. Malheureusement, tous les témoignages transmis à l’UFCM soulignent que l’interlocuteur insiste à plusieurs reprises sur la gratuité de la prestation. Or, dans les faits, cette dernière est payante puisque le coût de la communication est surtaxé. Ainsi, l’une des victimes qui nous a contacté, s’est retrouvée avec une facture téléphonique (hors forfait) de 1800 euros. Par conséquent, nous constatons que ces « roqyas » gratuites sont fondées sur la technique dite du « call-back » qui consiste à amener une personne à rappeler un numéro surtaxé, information qui lui est bien évidemment dissimulée. Une « roqya » peut être payante à condition de respecter un cadre prédéterminé, fondé sur l’information et la transparence des honoraires. En conclusion A la lumière des développements susvisés, l’UFCM appelle d’une part à une régulation du métier de la pratique de la « roqya », d’autre part, à la vigilance de chacun à ne pas céder à la tentation d’une « roqya » qui ne serait pas réalisée dans les conditions requises et qui pourrait produire des effets inverses. Au-delà du cadre spirituel ou juridique, les divers témoignages reçus et étudiés par l’UFCM ne peuvent pas nous laisser indifférents à la question suivante : pourquoi des personnes sont-elles amenées à accepter aussi facilement une « roqya » par téléphone ? Est-ce la gratuité qui a déterminé leur choix ? Certes le mal-être produit par cette société est de plus en plus grand. Nous vivons une époque où les êtres sont de plus en plus coupés des signes de Dieu et vivent un rythme de vie effréné. Ces affaires sont révélatrices des maux les plus profonds qui touchent la communauté musulmane. Par ailleurs, comme l’ensemble des rites islamiques (hajj, halal, pompes funèbres) censés nous rappeler les limites qui déterminent la voie vers Dieu, nous constatons que leur marchandisation trahit de plus en plus leur vocation première. Suffit-il qu’un interlocuteur se présente à nous comme un « cheikh » ou un imam et qu’il nous propose une « roqya » gratuite pour l’accepter aussitôt Ne devrions-nous pas tous nous interroger sur le fait qu’il y ait des musulmanes et des musulmans aussi isolés et aussi ignorants de leur propre religion pour être trompés aussi facilement ? Sommes-nous devenus si dépendants des Hommes que nous en oublions de nous adresser directement à Dieu pour solutionner nos malaises ? Autant de questions que chacun d’entre nous a la responsabilité de se poser. En effet, aucun de nous ou de nos proches ne sont à l’abri d’une telle tromperie. Il convient enfin de rappeler que la « roqya » est un remède précis et qu’elle ne peut se faire que sous certaines conditions et surtout qu’elle demeure l’exception à la règle, qui est de toujours s’adresser directement à Dieu. Avant de recourir à une « roqya », il convient de faire une introspection sur ses propres pratiques cultuelles et de revenir.

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