Boy Mow Chau's answer to Xiang Ning's Junior College 2 H2 Maths Singapore question.
note that this question is not about binomial distribution.
for binomial distribution, the probability of 'success' for each trial, must be constant.
to form the committee of 3, the men & women are selected from a small pool of 10. the probability of a particular committee member being a woman, is not a constant. for example, if there are 6 men and 4 women, the probability of the 1st member being woman is 4/10, but thereafter, the probability of the 2nd member being woman is 3/9. so the probability varies.
to answer this question, we need to go back to the basic definition of E(W) and Var(W).
E(W) = summation [ w P(W=w) ]
Var(W) = E (W^2) - [ E(W) ] ^2
for binomial distribution, the probability of 'success' for each trial, must be constant.
to form the committee of 3, the men & women are selected from a small pool of 10. the probability of a particular committee member being a woman, is not a constant. for example, if there are 6 men and 4 women, the probability of the 1st member being woman is 4/10, but thereafter, the probability of the 2nd member being woman is 3/9. so the probability varies.
to answer this question, we need to go back to the basic definition of E(W) and Var(W).
E(W) = summation [ w P(W=w) ]
Var(W) = E (W^2) - [ E(W) ] ^2
have you got any answer from your teacher regarding the committee of 14 people question which you posted last week?
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