46.The one-time fling! Have you ever purchased an article of clothing (dress, sp

Question

46.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 5% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of nine 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

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
P( X = 0 ) = ( 5 0 ) * ( 0.05^0) * ( 1 - 0.05 )^5
= 0.7738

b.
P( X < 1) = P(X=0)
= ( 5 0 ) * 0.05^0 * ( 1- 0.05 ) ^5
= 0.7738
P( X > = 1 ) = 1 - P( X < 1) = 0.2262

c.
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)
= ( 5 2 ) * 0.05^2 * ( 1- 0.05 ) ^3 + ( 5 1 ) * 0.05^1 * ( 1- 0.05 ) ^4 + ( 5 0 ) * 0.05^0 * ( 1- 0.05 ) ^5
= 0.9988

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