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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?

 Apr 19, 2019
 #1
avatar+106539 
+1

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

 

 

cool cool cool

 Apr 19, 2019
 #2
avatar+128 
-2

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

 Apr 21, 2019

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