Question

Ashley, Bob, Claire, and Daniel are among 13 students who entered a lottery to win a free vacation to Paris.

Only 4 people will be chosen at random. What is the probability that Ashley, Bob, Claire, and Daniel will be
chosen? (Lesson 19.3) (1 point)

Answer 1

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.

Explanation:

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

The order in which the students are chosen is not important, so the combinations formula is used 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:

4 students from a set of 4(Ashley, Bob, Claire, and Daniel). So

`D = C_(4,4) = (4!)/(4!(4-4)!) = 1`

Total outcomes:

4 students from a set of 13(number of students in the lottery). So

`T = C_(13,4) = (13!)/(4!(13-4)!) = 715`

Probability:

`p = (D)/(T) = (1)/(715) = 0.0014`

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.