谁统计学强悍的帮忙做做题目吧。！
Question 1
1. For married couples living in a certain region, the probability that the husband will vote
on a referendum is 0.35, the probability that the wife will vote is 0.39 and the probability
that they will both vote is 0.22. What is the probability that:
(a) At least one member of a married couple will vote?
(b) A husband will vote and his wife will not vote?
(c) A wife will vote, given that her husband will not vote?
State with justification whether or not the probability that a husband will vote is independent
of the probability that his wife will vote.
2. (a) A committee of size 10 is selected at random from 8 professional people and 12
non-professional people.
Write down expressions for and evaluate (to 4 decimal places) the following:
i. The probability that exactly 5 professional people are in the committee.
ii. The probability that at least 6 professional people are in the committee.
iii. The probability that exactly 6 professional people are in the committee, given
that at least 6 professional people are in the committee.
(b) A committee of size 10 is selected at random from 4,000 professional people and
6,000 non-professional people.
Write down a Binomial random variable X that can be used to approximate the
probability that x members of the committee are professional.
Hence, estimate the following, (giving your answers to 4 decimal places):
i. The probability that less than 5 professional people are in the committee.
ii. The probability that exactly 4 professional people are in the committee, given
that no more than 6 professional people are in the committee