SOLUTION: (a) From a stack of 3 dice, one is taken and rolled twice. If, unknown to the gambler, two of the dice are weighted and each have a 1/7 chance of rolling a 6, what is the probabil

Algebra ->  Probability-and-statistics -> SOLUTION: (a) From a stack of 3 dice, one is taken and rolled twice. If, unknown to the gambler, two of the dice are weighted and each have a 1/7 chance of rolling a 6, what is the probabil      Log On


   

Question 919689: (a) From a stack of 3 dice, one is taken and rolled twice.
If, unknown to the gambler, two of the dice are weighted and each have a 1/7 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 Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
For him to roll 2 6's, he will 

EITHER

1. choose a weighted die    <--probability = 2/3
AND
2. roll a 6 the first time  <--probability = 1/7
AND
3. roll a 6 the second time <--probability = 1/7

OR

1. choose a non-weighted die  <--probability = 1/3
AND
2. roll a 6 the first time  <--probability = 1/6
AND
3. roll a 6 the second time <--probability = 1/6

AND suggests multiplication and OR suggests addition:

%282%2F3%29%281%2F7%29%281%2F7%29%2B%281%2F3%29%281%2F6%29%281%2F6%29%22%22=%22%22121%2F5292

Approximately 0.023 

---------
 (b)

                                  P(weighted and (6 and 6) )
P(weighted die | rolled 2 6's) = ------------------------
                                      P(6 and 6)

The denominator is the result of part (a) 

= %28%282%2F3%29%281%2F7%29%281%2F7%29%29%2F%28121%2F5292%29 = %282%2F147%29%2F%28121%2F5292%29 = 72%2F121 = about 0.595

Edwin