Question

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Suppose there is a basket containing one apple and two oranges. A student randomly pick one...

Suppose there is a basket containing one apple and two oranges. A student randomly pick one fruit from the basket until the first time the apple is picked. (Sampling with replacement)

(a) What is the sample space for this experiment? What is the probability that the student pick the apple after i tosses?

(b) What is the expected number of times the students need to pick the apple?

(c) Let E be the event that the first time an apple is picked up is after an even number of picks. What set of outcomes belong to this event? What is the probability that E occurs?

Solutions

Expert Solution

This is Sampling with replacement (i.e, the fruit is placed back to the basket after each pick).

Let stand for orange and stand for apple.

a) The sample space would be .

The probability of choosing apple in one pick is .

The probability that the student pick the apple after tosses is

Clearly, the random variable (the number of picks required to pick the first apple) has geometric distribution.

b) The expected value of the random variable is

. (Use formula for expectation for geometric distribution).

c) The outcome is the set .

The probability ,

The probability is the sum of infinite geometric series with common ratio .

The sum is

milcah answered 7 months ago

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