SOLUTION: 3. Suppose that you roll a fair die 5 times. What are the odds that you roll a) Exactly 4 sixes b) At least 4 sixes.

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Question 1185443: 3. Suppose that you roll a fair die 5 times. What are the odds that you roll
a) Exactly 4 sixes
b) At least 4 sixes.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


a) exactly 4 sixes

The probability of a 6 on each roll is 1/6; the probability of any other outcome is 5/6.

The number of orders in which you can get exactly 4 sixes in 5 rolls is C(5,4).

P(4 sixes in 5 rolls) = C%285%2C4%29%28%281%2F6%29%5E4%29%28%285%2F6%29%5E1%29=5%285%2F6%5E5%29=25%2F6%5E5=25%2F7776

ANSWER: 25/7776

b) at least 4 sixes

To the answer for part a, add the probability of getting sixes on all 5 rolls.

P(5 sixes on 5 rolls) = %281%2F6%29%5E5=1%2F7776

ANSWER: 26/7776 (simplify if required)