Answer:
10/21
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