A public opinion poll surveyed a sample of 1000 voters. The table below shows the number of males and females supporting Party A, Party B and Party C.
Party A Party B Party C Male 200 130 70 Female 250 350 50
(a) One of the voters is chosen at random. Events A, C and M are defined as follows:
A: the voter chosen supports party A
C: The voter chosen supports Party C.
M: The voter chosen is a male
Find (i) , (ii) .
Determine whether A and M are independent.
(b) It is given that in the sample, 20% of Party A supporters, 30% of Party B supporters and 5% of Party C supporters are immigrants.
(i) One of the voters selected from the sample at random is an immigrant. What is the probability that this voter supports Party A?
(ii) Three voters are chosen from the sample at random. Find the probability that there is exactly one immigrant voter who supports Party C or exactly one female who supports Party A (or both).
Should the answer for part (b)(ii) be 0.4325370019 or 0.433683438?