Question

Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs and mutually exclusive.

P(A)P(B)P(C)=0.42=0.25=0.01P(A|B)P(C|B)P(A|C)=0=0.01=0.42
A. B and C are independentB. A and C are mutually exclusiveC. A and B are independentD. A and C are independentE. B and C are mutually exclusiveF. A and B are mutually exclusive

Answer 1

Answer: A. B and C are independent; D. A and C are independent; F. A and B are mutually exclusive

Explanation: Independent events are events that occurs without one influencing the other. The following shows the conditions for events to be independent:

P(1∩2) = P(1)P(2)

P(1∪2) = P(1) + P(2) - P(1)P(2)

P(1|2) = P(1)

P(1|¬2) = P(1)

Since, according to the question:

P(C|B) = 0.01

P(A|C) = 0.42

follows one of the conditions above, it can be concluded that:

C and B are independents and A and C are also independents.

Mutually exclusive events are those which can't happen at the same time. The conditions for it to be true are:

P(1∩2) = 0

P(1∪2) = P(1) + P(2)

P(1|2) = 0

P(1|¬2) =
`(P(1))/(1-P(2))`

Since:

P(A|B) = 0 satisfies one of the conditions, it can be concluded:

A and B are mutually exclusive.