Could someone please HELP me with this question?!?

Question

The probability that a customer will actually buy a pair of shoes if she tries them on is 0.3. What is the probability that Sapna will sell exactly 12 pairs of shoes if she waits on 25 customers who try on shoes?

Answer 1

Let X = number of pairs sold out of 25

X ~ Bin( 25 , 0.3 )

Pr(X = 12) = 25C12 times 0.3^12 times 0.7^13

= 0.0268 (i.e. about 3%)

Answer 2

Assuming customers will only buy one pair each, then
P(selling exactly 12 pairs) =
P(12 pairs sold AND 13 people don't buy) =
P(12 pairs sold) * P(13 don't buy) =
(0.3)^12 * (0.7)^13 * (25! / 12! 13!) =
About 0.0268

The (25!/12!13!) number is important because that's how many different ways you can get 12 customers out of 25 people.

Answer 3

This is a binomial problem. You need to solve (0.3 + 0.7)^25 and find the coefficient of the term 0.3^12

If you try to simply multiply 25 with 0.3, you will get 7.5 as the probable number of customers who buy the shoes. That is not a correct solution.

Answer 4

P(x) = nCx * p^x * q^(n-x)

n = number of trials
x = number of successes among n trials
p = probability of success in any one trial
q = probability of failure in any one trial (q = 1 - p)
nCx = combinations of n items, choose x

n=25
x=12
p=0.3
q=0.7
25C12= 25!/(12!*13!) = 5,200,300

P(12)=5200300*(0.3)^12*(0.7)^13

P(12) = 0.0268 = 2.68%