Question

A shipment of fifteen smartphones contains seven with cracked screens. If sold in a random order. What is the probability that exactly five of the first nine sold have cracked screens

Answer 1

29.37% probability that exactly five of the first nine sold have cracked screens

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the smartphones are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

5 with cracked screens, from a set of 7.

9-5 = 4 with good screens, from a set of 15-7 = 8.

So

`D = C_(7,5)*C_(8,4) = (7!)/(5!(7-5)!)*(8!)/(4!(8-4)!) = 1470`

Total outcomes:

Nine phones, from a set of 15. So

`T = C_(15,9) = (15!)/(9!(15-9)!) = 5005`

Probability:

`p = (D)/(T) = (1470)/(5005) = 0.2937`

29.37% probability that exactly five of the first nine sold have cracked screens