Question

The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 10% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of seven 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


(c) no more than two people have done a one-time fling

Answer 1

The trails are limited- n = 7

p = probability of doing a one-time fling = 0.1

1-p = probability of not doing a one-time fling = 0.9

This follows a binomial distribution with P(X=x) = C(n,x)*p^x*(1-p)^n-x

a) No one does it

P(X=0) = C(7,0)*(0.1)^0*(0.9)7 = 0.4782

b) At least one does it

P(X=1)+P(X=2)+....P(X=7)

This is also equivalent to 1-P(X=0)

i.e. 1-0.4782 = 0.5218

c) Not more than two have done it

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

P(X=1) = C(7,1)*(0.1)^1*(0.9)^6 = 0.372

P(X=2) = C(7,2)*(0.1)^2*(0.9)^5 = 0.124

So, no more than two does it = 0.4782+0.372+0.124 = 0.9742

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