Question

In one of its Spring catalogs, L.L. Bean® advertised footwear on 26 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked more than once.

1. Is it probable that all twenty will advertise footwear on them? Why or why not? (Round your answer to two decimal places.)

____ , because the probability that all twenty will advertise footwear is _____

2. What is the probability that you only need to survey at most five pages in order to find one that advertises footwear on it? (Round your answer to four decimal places.)

3. How many pages do you expect to need to survey in order to find one that advertises footwear? (Round your answer to the nearest whole number.)

Answer 1

Given,

Probability of success, p = 26/192 =0.1354

Number of trails, n = 20

Let x denote the random variable with binomial distribution given as,

Binomial distribution

​​​​​​

1.

No, it is not probable that that all twenty will advertise footwear on them.

​​​​​​P(X = 20) = 0.0

because the probability that all twenty will advertise footwear is 0.0

2. Probability that you only need to survey at most five pages in order to find one that advertises footwear on it,

Let x denote a rondom variable with Geometric distribution then,

The required probability is,

P(X ⩽ 5) = P(X=1) +P(X=2) +P(X=3) +P(X=4) +P(X=5)

P(X ⩽ 5) = 0.5823

3.

Number of pages expected to need to survey in order to find one that advertises footwear,

= 7.3855

= 7 pages.