Question

Given that: P(A) = 7/50= 0.14

P(B) = 10/50 = 0.2

P(A ∩ B) = 0.1

P(A ∪ B) = 0.24

P(western state) = 24/50

P(eastern state) = 26/50

Person A has been to 5 western states and 2 eastern states

Person B has been to 7 western states and 3 eastern states

Please answer the following with clear explanations:

k) Determine the conditional probability that both persons have visited the (randomly selected) state, given that at least one of them has visited it.

i) 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.

m) 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.

Answer 1

k)

The required conditional probability = = 0.1/0.24 = 5/12

i)

The conditional probability that A has visited the state, given that the state lies to the west of the Mississippi River

= P(A and western state)/P(western state) = 5/24

The conditional probability that A has visited the state, given that the state lies to the east of the Mississippi River

= P(A and eastern state)/P(eastern state) = 2/26

This means that their is higher chances that A visit a state that lies to the west of the Mississippi River as compared to the state that lies to the east of the Mississippi River.

m)

No, it is not independent.

Since the probability that A has visited the state, given that the state lies to the west of the Mississippi River and the probability that A has visited the state, given that the state lies to the east of the Mississippi River are different.