# Probabilty question

#### yeoky

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?

Thank you.

#### HallsofIvy

MHF Helper
You say "A public opinion poll surveyed a sample of 1000 voters" but your table has 1050 people, 400 men and 650 women.

#### yeoky

Sorry! There was a typo-error. It should be 300 instead of 350. Thank you Hallsfivy!

#### HallsofIvy

MHF Helper
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 250 300 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
There are 1000 voters and 200+ 250 support party A.

C: The voter chosen supports Party C.
There are 1000 voters and 70+ 50 support party C.

M: The voter chosen is a male
There are 1000 voters and 200+ 130+ 70 are male.

Find (i) , (ii) .
I have no idea what "(i)" and "(ii)" refer to.

Determine whether A and M are independent.
You have determined the probability of A and M separately. Multiply them together. Now, from the chart, there are 1000 voters and 200 of them are men who support party A. Is that probability the same as the answer you got by multiplying?

(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?
There are 200+ 250= 450 supporters of party A. 20% of 450 is 90. There are 130+ 300= 430 supporters of party B. 30% of 430 is 129. There are 70+ 50= 120 supporters of party C. 5% of 120 is 6. So there are a total of 90+ 129+ 6= 225 immigrant voters of whom 90 support 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).
Writing "C" for "immigrant voter who supports party C", "A" for "female voter who supports party A", and "B" for "neither one of those", we might have CBB, BCB, BBC, or ABB, BAB, BBA, or, ABC, ACB, BAC, BCA, CAB, CBA. You can find the probability of "A",
"B", or "C" separately and then find the probability of each of those 3 voter patterns.

Should the answer for part (b)(ii) be 0.4325370019 or 0.433683438?

Thank you.

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