Question

	Person B has visited	Person B has not visited	Total
Person A has visited	2	0	2
Person A has not visited	0	48	48
Total	2	48	50

Now suppose that one of the 50 states is selected at random, so each state has a 1/50 = .02 probability of being selected.

1. Determine the conditional probability that A has visited the (randomly selected) state, given that the state lies to the west of the Mississippi River. Then determine this conditional probability, given that the state lies to the east. Comment on how these conditional probabilities compare, and what that means in this context.

2. Is whether or not person A visited a state independent of whether the state lies to the east or west of the Mississippi River? Justify your answer.

3. Determine the conditional probability that the (randomly selected) state lies to the west of the Mississippi River, given that A or B has visited the state.

4. Determine the conditional probability that the (randomly selected) state lies to the west of the Mississippi River, given that A and B have visited the state.

Answer 1

(a) probability of A visiting any given state = 2/50 = 0.04

therfore,

probability of A visiting any given state that lies west of mississippi = 2/50 = 0.04

probability of A visiting any given state that lies east of mississippi = 2/50 = 0.04

the probabilities are same because A having visited any state has same probability regardless of it being east or west

(b)person A visited a state is independent of whether the state lies to the east or west of the Mississippi River because A having visited any state has same probability regardless of it being east or west

(c)

the P(A or B visited) = P(A and B visited) + P(A visited , B not visited) + P(B visited, A not visited)

P(A or B visited) = 2/50 + 0 + 0

P(A or B visited) = 0.04

P(state lies to west) = 22/50 {22 states out of 50 are west of mississippi}

P((state lies to west) AND (A or B visited)) = (22/50) * 0.04 = 44/2500

(d) P(A and B visited) = no fo states A and B both visited / 50

P(A and B visited) = 2/50 = 0.04

P((state lies to west) AND (A and B visited)) = (22/50) * 0.04 = 44/2500

P.S. (please upvote if you find the answer satisfactory)