Probability

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Probability

by nidhis.1408 » Thu Jul 12, 2012 8:51 am
For one roll of a certain die, the probability of rolling a two is 1/6. If this die is rolled
4 times, which of the following is the probability that the outcome will be a two at
least 3 times?
(A) (1/6)4
(8) 2(1/6i + (1/6)4
(C) 3{1/6)3(5/6) + (1/6)4
(O) 4{1/6)3{5/6) + (1/6)4
(E) 6{1/6)3{5/6) + (1/6)4
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by Anurag@Gurome » Thu Jul 12, 2012 10:33 pm
nidhis.1408 wrote:For one roll of a certain die, the probability of rolling a two is 1/6. If this die is rolled 4 times, which of the following is the probability that the outcome will be a two at least 3 times?
Probability that the outcome will be a two at least 3 times = P
Probability that the outcome will be a two exactly 3 times = P(3)
Probability that the outcome will be a two exactly 4 times = P(4)

P(3) = [4C3]*[(1/6)^3]*[(5/6)^1] = 4[(1/6)^3]*[5/6]
[We have multiplied 4C3 because this is the number of different ways to get 3 twos in four throws.]
P(4) = [(1/6)^4]

Now, P = P(3) + P(4) = 4[(1/6)^3]*[5/6] + [(1/6)^4]

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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