The onetime fling Have you ever purchased an article of clot

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 aone-time fling. About 5% 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

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

Solution

a)

P(no one) = (1-0.05)^10 = 0.598736939 = 0.599 [answer]

b)

P(at least one) = 1 - P(no one) = 1 - 0.599 = 0.401 [answer]

c)
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.05      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.988496443 [answer]