A survey showed that a majority of Americans plan on doing their holiday shopping online because theydon’t want to spend money on gas driving from store to store. Suppose we have a group of 10 shoppers; 7prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A randomsample of 3 of these 10 shoppers is selected for a more in-depth study of how the economy has impactedtheir shopping behavior.a) What is the probability that exactly two prefer online shopping?b) What is the probability that the majority (either two or three) prefer shopping online?

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Asked Nov 26, 2019
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A survey showed that a majority of Americans plan on doing their holiday shopping online because they
don’t want to spend money on gas driving from store to store. Suppose we have a group of 10 shoppers; 7
prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A random
sample of 3 of these 10 shoppers is selected for a more in-depth study of how the economy has impacted
their shopping behavior.
a) What is the probability that exactly two prefer online shopping?
b) What is the probability that the majority (either two or three) prefer shopping online?

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Expert Answer

Step 1

Hypergeometric distribution is a discrete probability distribution which describes the probability of getting k successes in n draws of sampling without any replacement from a population whose size is N.

 The probability mass function to calculate the probability of getting k successes in n draws without any replacement from the population whose size is N is,

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(к\(N-K kп-k NA Р(X 3Dк) -. п

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Step 2

Here, N is the population size, n is the sample size (number of draws), k is the number of successes in n draws, and K is the number of successes in the population.

Step 3

(a)

Here, N = 10, n = 3, k = 2, K = 7

Consider, X be the random variable that represents the number of Americans that prefer onli...

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K (N -K P(X 2) = 7 10-7 2 3-2 10 3 21 x3 120 0.525

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