Question

in a sample of 80 adults, 25 said that they would buy a car from a friend. three adults are selected at random without replacement. find the probability that none of the three would buy a car from a friend.

Answer 1

Answer:

31.9%

Step-by-step explanation:

We have that,

Total number of adults = 80

Number of people that would buy a car from a friend = 25

So, the number of people that would not buy a car from a friend = 80-25 = 55.

Since, three people are selected randomly.

Thus, the probability that none of them would buy a car from a friend is given by,

$\frac{\binom{55}{3}}{\binom{80}{3}}$

i.e. $\frac{\frac{55!}{3!\times 52!}}{\frac{80!}{3!\times 77!}}$

i.e. $\frac{55!\times 3!\times 77!}{3!\times 52!\times 80!}$

i.e. $\frac{55\times 54\times 53}{80\times 79\times 78}$

i.e. $\frac{157410}{492960}$

i.e. 0.319

Thus, the probability of people who would not buy a car from a friend is 0.319 i.e. 31.9%