SOLUTION: (a) From a stack of 3 dice, one is taken and rolled twice. If, unknown to the gambler, one of the dice is weighted and has a 1/9 chance of rolling a 6, what is the probability tha

Question 806240: (a) From a stack of 3 dice, one is taken and rolled twice.
If, unknown to the gambler, one of the dice is weighted and has a 1/9 chance of rolling a 6, what is the probability that the gambler rolls two 6's?
(b) If the gambler has rolled two sixes, what is the probability that he has rolled the weighted die?

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a)
If weighted die is rolled the probability of rolling 2 sixes:(1/9)^2=1/81.
If non-weighted die is rolled the probability of rolling 2 sixes:(1/6)^2=1/36.
(1/81 + 2/36)/3
= (36/2916 + 162/2916)/3
= 11/162 * 1/3
=11/486 the probability that the gambler rolls two 6's
.
b)
36/(36+162) The numerators of the fractions in part a).
=2/11 the probability that he has rolled the weighted die.
.
Ed
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