(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

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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