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The CDC estimates that a non-infected person has a 10% chance of contracting mumps from an infected person from even a brief encounter. What is the probability that a non-infected person contracts mumps after 9 brief encounters with infected people?

Question

The CDC estimates that a non-infected person has a 10% chance of contracting mumps from an infected person from even a brief encounter. What is the probability that a non-infected person contracts mumps after 9 brief encounters with infected people?

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Step 1

The random variable X follows geometric distribution with probability 0.10. The geometric distribution is,

P(X x)-(1-p) p
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P(X x)-(1-p) p

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Step 2

The probability that a non-infected person contracts mumps...

P(X 9)(1-0.10) (0.10)
= 0.3874(0.10)
=0.03874
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P(X 9)(1-0.10) (0.10) = 0.3874(0.10) =0.03874

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Probability

Basic Probability

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