You have 2 boxes that contains 100 balls each, and the balls can be white, blue, red, or half red an

Kellen Perkins

Kellen Perkins

Answered question

2022-05-29

You have 2 boxes that contains 100 balls each, and the balls can be white, blue, red, or half red and blue.
Box A contains: 90 white balls, 10 red balls
Box B contains: 86 white balls, 4 red balls, 9 blue balls, 1 red and blue ball
If you don't know which box you pick a ball from (the probability is equal for what box you chose), what is the probability for pulling exactly 2 white balls and 1 red ball, if you don't put it back and don't take a look at the balls until all 3 are pulled from the box you chose? (You only pick 3 balls).
I thought this would be pretty straight forward by using combinatorics:
P(1 red and 2 white balls) = ( 176 2 ) ( 200 3 )

Answer & Explanation

Maximo Sweeney

Maximo Sweeney

Beginner2022-05-30Added 7 answers

X be the event "you draw 2 white balls and one red ball" Also, let A be the event "you draw from box A" and B be the event "you draw from box B.
Then, as a certain Bayes might tell you, because A and B represent a partition (their union is the universe set, their intersection is empty), that
P ( X ) = P ( X | A ) P ( A ) + P ( X | B ) P ( B )

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