What is the probability a server will refuse to serve alcoholic beverages to exactly 2 minors if he randomly checks the IDs of 5 of the 9 students in the establishment, and 4 of the 9 students are minors?

10/21

Step-by-step explanation:

Probability = Expected outcome/total outcome

If he randomly checks the IDs of 5 of the 9 students in the establishment, the total outcome will be expressed as:

9C5 = 9!/4!5!

9C5 = 9×8×7×6×5!/5!×24

9C5 = 9×8×7×6/24

9C5 = 126

Total outcome = 126

For the expected

First we know that 4out of 9 students are minor, and we want to know the probability that exactly 2 are minor, this can be done in 4C2 ways

4C2 = 4!/2!2!

4C2 = 4×3×2/4

4C2 = 6

Also since 4 out of 9 are minor, then 5 are not minor and if out of every 5, exactly two are minor, then 3 are not.

Those not minor can be expressed in 5C3 ways

5C3 = 5!/2!3!

5C3 = 5×4×3!/2×3!

5C3 = 20/2

5C3 = 10

Total expected outcome = 4C2 × 5C3

Total expected outcome= 6×10 = 60

Hence, the probability a server will refuse to serve alcoholic beverages to exactly 2 minors will be;

= 60/126

= 30/63

= 10/21

312312

step-by-step explanation: