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 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of eight 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

a) 0.2725

b) 0.7275

c) 0.8948

Explanation:

This is a binomial distribution probability problem. The formula is:

`P(x)=(n!)/((n-x)!x!)p^(x)q^(n-x)`

Where

n is the number of trials [here we are taking 8 person, so n = 8]

x is what we are looking for [in the problem]

p is the probability of success [ 15%, so p = 0.15

q is the probability of failure [q = 1-p = 0.85]

Now,

a)

We are looking for "no one" did fling, so x = 0

Let's put into formula and find out the probability:

`P(x=0)=(8!)/((8-0)!0!)(0.15)^(0)(0.85)^(8)\\P(x=0)=0.2725`

So, the probability that no one has done a one-time fling is 0.2725

b)

Atleast 1 person means P(x ≥ 1).

This can be found by:

P(x ≥ 1) = 1 - P(x=0) = 1 - 0.2725 = 0.7275

THus, Probability that at least one person has done a one-time fling is 0.7275

c)

No more than 2 people means P (x≤2).

This is essentially

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2)

P ( x = 0 ) is found in part (a), which is 0.2725

P (x = 1 ) and P(x=2) can be found using formula:

`P(x=1)=(8!)/((8-1)!1!)(0.15)^(1)(0.85)^(7)\\P(x=1)=0.3847`

and

`P(x=2)=(8!)/((8-2)!2!)(0.15)^(2)(0.85)^(6)\\P(x=2)=0.2376`

Thus,

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2) = 0.2725 + 0.3847 + 0.2376 = 0.8948