There is a box with 12 dice which all look the same. However there are actually three types of dice:

Brenton Dixon 2022-07-21 Answered
There is a box with 12 dice which all look the same. However there are actually three types of dice:
6 normal dice. The probability to get a 6 is 1 / 6 for each dice.
3 biased dice. The probability to get a 6 is 0.85. 3 biased dice. The probability to get a 6 is 0.05.You take a die from the box at random and roll it.What is the conditional probability that it is of type b, given that it gives a 6?
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Answers (1)

bgr0v
Answered 2022-07-22 Author has 13 answers
P ( 6 ) = P ( 6 | A ) P ( A ) + P ( 6 | B ) P ( B ) + P ( 6 | C ) P ( C )
That is, the chance of rolling a six is the chance of rolling a 6 on dice A times the chance of choosing dice A. And then same for B, and for C
P ( 6 ) = 1 6 1 2 + 17 20 1 4 + 1 20 1 4 = 37 120
What is the chance that you rolled dice B given that you rolled a 6?
P ( B | 6 ) = P ( 6 | B ) P ( B ) P ( 6 ) 17 20 1 4 37 120 = 51 74 0.70
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