We consider 7 bags each containing 6 balls. Each ball is numbered from 1 to 6....

We consider 7 bags each containing 6 balls. Each ball is numbered from 1 to 6. The first 6 bags contain 6 balls where all numbers from 1 to 6 are present. The 7th bag contains 6 balls that all have the same number equal to 6. You take a bag randomly. You shoot a ball and put it back in its bag. You shoot another ball and you put it back in his bag and you observe that the two balls have the number 6. What is the probability of choosing the 7th bag?

On considère 7 sacs contenant chacun 6 balles. Chaque balle est numérotée de 1 à 6. Les 6 premiers sacs contiennent 6 balles où tous les numéros de 1 à 6 sont présents. Le 7-ième sac contient 6 balles qui ont toutes le même numéro égal à 6. Vous prenez un sac au hasard. Vous tirez une balle et vous la replacez dans son sac. Vous tirez une autre balle et vous la replacez dans son sac et vous observez que les deux balles ont le numéro 6. Quelle est la probabilité de choisir le 7-ième sac ?

Expert Solution

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Bayes Theorems Led E, denote the probability of choosing Es dooote the probability of choosing a ball from Bag 1 a ball from Bagai Ez dosolo the probability of chooslog a ball & then we have (each bag is chooses randonly) - P(E)=P(E2) = P(E3 ... 2P (E) 117. 4 be the 1st ball takoo from this bas A. be the Ind ball taken from this bas Now, we are gives that, Both Aland As all bi so let, I be the event that both balls Aland Az are 6. Then we bove, Ale 6 and 1226 gives that, the the probabilty of P(I)El P(FJEI - bag is ! - P(FIE) - P(AIZGDA26 ) { Now, since, the Bagl contains bballs numbered 1 to 6. and the ball is selected randossly, then P(A1= 6) = 16 And after shooting, a ball is replaced which fersthee imphis that P(A22.6 / Now, both these procentes doeerst depend on each other: reolselecting first ball is odlopendest a selecting subod ball) - No change in probability > PLAI-60 = 6 - 1x4 & 1/36

milcah answered 1 year ago

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