Need help with 32 Voting Patterns The following data show th

Voting Patterns The following data show the number of voters in a sample of 1000 from a large city, categorized by religion and their voting preference. Find the probability a person is a Democrat. Find the probability a person is a Catholic. Find the probability a person is Catholic, knowing the person is a Democrat. Are the events R and D independent? Are the events P and R independent?

Solution

A)

P(D) = 400/1000 = 0.4

B)

P(C) = 400/1000 = 0.4

C)

P(C|D) = 160/400 = 0.4

D)

Here,

P(R) = 400/1000 = 0.4

P(R|D) = 0 [mutually exclusive]

As P(R) =/= P(R|D), hence, NO, THEY ARE NOT INDEPENDENT.

E)

As

P(P) = 500/1000 = 0.5
P(P|R) = 220/400 = 0.55

As P(P) =/= P(P|R), then NO, THEY ARE NOT INDEPENDENT.