Question

A Field Poll Survey reported that 53% of registered voters in a state approved of allowing two people of the same gender to marry and have regular marriage laws apply to them. Among 18 to 39 year olds (registered voters in this state), the approval rating was 76%. Seven in ten registered voters in this state said that the upcoming Supreme Court's ruling about the constitutionality of a proposition was either very or somewhat important to them. Out of those registered voters who support same-sex marriage, 73% say the ruling is important to them. In this problem, let the following apply.

•	C = registered voters who support same-sex marriage
•	B = registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them
•	A = registered voters who are 18 to 39 years old.

1. Find P(C|A). (Enter your answer to two decimal places.)

2. Find P(B|C). (Enter your answer to two decimal places.)

3. Find P(C AND B). (Enter your answer to four decimal places.)

4. Find P(C OR B). (Enter your answer to four decimal places.)  

Answer 1

From given information we have

P(C) = 0.53, P(B) = 7/10 = 0.70, P(C| A ) = 0.76, P(B | C) = 0.73

1:

The probability that registered voters who support same-sex marriage, given that registered voters who are 18 to 39 years old is

P(C|A) = 0.76

2:

The probability that  registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them given that person is registered voters who support same-sex marriage is

P(B |C) = 0.73

3:

P(C and B) = P(B|C)P(C) = 0.73 * 0.53 = 0.3869

4:

P(C or B) =P(C) + P(B) - P(C and B) = 0.53 + 0.70 - 0.3869 = 0.8431