Two Basic Rules of Probability · Exercise 11

Prior to the 2015 Supreme Court decision legalizing same-sex marriage nationwide, a survey reported that 61% of California registered voters 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 (California registered voters), the approval rating was 78%. Six in ten California registered voters said that the upcoming Supreme Court’s ruling about the constitutionality of California’s Proposition 8 was either very or somewhat important to them. Out of those CA registered voters who support same-sex marriage, 75% say the ruling is important to them.
In this problem, let:

• C = California registered voters who support same-sex marriage.
• B = California registered voters who say the Supreme Court’s ruling about the constitutionality of California’s Proposition 8 is very or somewhat important to them
• A = California registered voters who are 18 to 39 years old.

(a) Find P(C).
(b) Find P(B).
(c) Find P(C$|$A).
(d) Find P(B|C).
(e) In words, what is C$|$A?
(f) In words, what is B$|$C?
(g) Find P(C $\cap$ B).
(h) In words, what is C $\cap$ B?
(i) Find P(C $\cup$ B).
(j) Are C and B mutually exclusive events? Show why or why not.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §3.3 Two Basic Rules of Probability · Exercise 11