The one-time fling! Have you ever purchased an article of clothing dress, sports

Question

The one-time fling! Have you ever purchased an article of clothing dress, sports acket, etc , worn the item once to a party, and then returned the purchase? This is called a one-time fing. About 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of ten adult friends, what is the probability of the following? (Round your answers to three decimal places.) (a) no one has done a one-time fling (b) at least one person has done a one-time fling 04012x (c) no more than two people have done a one-time fling

Explanation / Answer

n = 10

p = 0.15

It is a binomial distribution.

P(X = x) = nCx * px * (1 - p)n - x

a) P(X = 0) = 10C0 * (0.15)^0 * (0.85)^10 = 0.1969

b) P(X > 1)

= 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - (10C0 * (0.15)^0 * (0.85)^10)

= 1 - 0.1969

= 0.8031

c) P(X < 2)

= P(X = 0) + P(X = 1) + P(X = 2)

= 10C0 * (0.15)^0 * (0.85)^10 + 10C1 * (0.15)^1 * (0.85)^9 + 10C2 * (0.15)^2 * (0.85)^2

= 0.8202

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