+31 A committee of 3 members is selected from a club made up of
18
junior members and
12
senior members. What is the expected number of juniors in the committee?
+128408 Total number of possible committees = 30C3 = 4060
Number of committees with 0 junior members = 12C3 = 220
Number of committees with 1 junior member and 2 senior members = 18C1 * 12C2 = 1188
Number of committes with 2 junior members and 1 senior member = 18C2 * 12C1 = 1836
Number of committees with 3 junior members = 18C3 = 816
Expected number of juniors =
0*(220/4060) + 1* (1188/4060) + 2* ( 1836/4080) + 3 *(816/4060) ≈ 1.8
+220 To find the number of expected juniors to come in the committee, we have to figure out the total amount of members. 18+12 is 30. There are 30 members. Now 30/3, which is the amount of people in a committee(I mean the 3), is 10. 18 divided by 10 is 1.8 junior members expected.
~~Hypotenuisance
