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The proportion of households in the US that own both at cat and a dog is...

The proportion of households in the US that own both at cat and a dog is .20. Suppose you randomly pick one household at a time until you find a household that owns both a cat and a dog. Verify that the distribution of the random variable X that counts the number of trials needed until you pick the first household that owns both a cat and a dog can be considered a geometric distribution. b. What is the probability that you pick a household that owns both a cat and dog on your first trial? c. What is the probability that you pick the first household that owns both a cat and a dog on your fourth trial?

Math   Statistics-And-Probability   
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Answer #1

here as we are picking the households till we find the desired result . Also probability of each event is fixed and independent from trail to trail ; therefore this is a geometric distribution

b)

robability that you pick a household that owns both a cat and dog on your first trial =0.20

c)

probability that you pick the first household that owns both a cat and a dog on your fourth trial

=P(not on first 3 trails and first success on 4th trail)=(0.8)3*0.2 =0.1024

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