Question

In a group of 40 people, 35% have never been abroad. Two people are selected at random without replacement and are asked about their past travel experience. a. Is this a binomial experiment? Why or why not? b. What is the probability that in a random sample of 2, no one has been abroad?

Answer 1

Answer:

$\frac{7}{60}$

Step-by-step explanation:

Given that in a group of 40 people, 35% have never been abroad. Two people are selected at random without replacement and are asked about their past travel experience.

Since the two are drawn without replacement the first trial affects the second trial.  In other words, each trial is not independent of the other.

a) Hence this cannot be binomial experiment.  The reason is p=probability for each trial is not constant as first draw affect the probability for Ii draw

b) The probability that in a random sample of 2, no one has been abroad

=Prob of selecting both people from the group where no one has been abroad

We have in the group 35% i.e. 14 people never been to abroad

So required probability = Prob of selecting both from 14 people

=$\frac{14C2}{40C2} \\=\frac{14*13}{40*39} \\=\frac{7}{60}$