A committee of four students will be selected from a list that contains six Grade 9 students and eight Grade 10 students. a) Show the probability distirubtion for the number of grade 10's on the comittee. b) What is the expected number of Grade 10 students on the committee?     

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(1) We find the probability that there are 0,1,2,3,or 4 grade 10 students on the committee.

The probability of a randomly chosen student being in grade 10 is 8/14, so p=8/14 and q=6/14.

The probability that a given number k of students on the committee is from grade 10 is...

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(1) We find the probability that there are 0,1,2,3,or 4 grade 10 students on the committee.

The probability of a randomly chosen student being in grade 10 is 8/14, so p=8/14 and q=6/14.

The probability that a given number k of students on the committee is from grade 10 is `P(k)=` `_4C_kp^kq^(4-k)`

``x         0         1            2          3            4
----------------------------------------------

P(x)   .034      .180      .360       .320      .106

(2) The expected value of grade 10 students is the mean of the probability distribution. (Treat the distribution like a weighted distribution and find the weighted mean, noting that the sum of the "weights" is 1.)

`mu=sum x*P(x)~~2.286`

Thus the expected value of grade 10 students is 2.286

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