Financial Risk Manager Part 1
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Given the experiment of rolling a die until the number 6 appears, what is the probability that it takes at least 3 rolls?
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Community
NNikitesh
A
1/12
B
1/3
C
11/36
D
25/36
Explanation:
The probability that it takes at least 3 rolls to get a 6 is calculated as:
P(at least 3 rolls) = 1 - P(less than 3 rolls)
P(less than 3 rolls) = P(getting 6 in 1st roll) + P(getting 6 in 2nd roll)
P(getting 6 in 1st roll) = 1/6
P(getting 6 in 2nd roll) = (5/6) × (1/6) = 5/36
So P(less than 3 rolls) = 1/6 + 5/36 = 6/36 + 5/36 = 11/36
Therefore, P(at least 3 rolls) = 1 - 11/36 = 25/36
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