1. Using a single roll of a die, find an example of two events (collections of o

Question

1. Using a single roll of a die, find an example of two events (collections of out-comes), A and B, where P(A|B) = P(B|A) > 0 but the two events are not independent. (Hint: you need to show that P(A) does not equal P(A|B))
1. Using a single roll of a die, find an example of two events (collections of out-comes), A and B, where P(A|B) = P(B|A) > 0 but the two events are not independent. (Hint: you need to show that P(A) does not equal P(A|B))
1. Using a single roll of a die, find an example of two events (collections of out-comes), A and B, where P(A|B) = P(B|A) > 0 but the two events are not independent. (Hint: you need to show that P(A) does not equal P(A|B))
1. Using a single roll of a die, find an example of two events (collections of out-comes), A and B, where P(A|B) = P(B|A) > 0 but the two events are not independent. (Hint: you need to show that P(A) does not equal P(A|B))

Explanation / Answer

P(A) = prob of getting a even number = 3/6 = 1/2

P(A|B) = prob of getting even and greater than 3 = getting 4,6 / 4,5,6 = 2/3

Since 1/2 != 2/3 the 2 events aren't independent.

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