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
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-> 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
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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?
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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
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b)
36/(36+162) The numerators of the fractions in part a).
=2/11 the probability that he has rolled the weighted die.
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Ed
