Define conditional probability of event A, given that event B has occurred.

A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw B : 6 on the first and 5 on the second throw Find the probability of A given that B has already occurred.

The probability of event A is 3//4 . The probability of event B , given that event A occurs is 1//4 . The probability of event A , given that event B occurs is 2//3 . The probability that neither event occurs is

If P(A - B) = 1/3,P(A) =1/2 and P(B) =1/3 ,find the probability that out of the events A and B. Only the event B occurs.

The probability of an event may exceed unity.

For the three events A ,B , and C , P (exactly one of the events A or B occurs)= P (exactly one of the two evens B or C )= P (exactly one of the events C or A occurs)= p and P (all the three events occur simultaneously)= p^2 where 0 < p < 1//2 . Then the probability of at least one of the three events A , B and C occurring is

can 7/2 be the probability of an event? Explain.

If A and B are any two events such that P(A) = 2/5 "and" P(A cap B) = 3/20 then the conditional probability P(A //A' cup B') where A denotes the complement of A is equal to

If P(A//B)=(1)/(3), P(B)=(1)/(4) and P(A)=(1)/(2) , find the probability that exactly one of the events A and B occurs.

if P(A|B) = 1/3 , P(A) = 1/4 and P(B) = 1/2, find the probability that exactly one of the events A and B occurs.

The following Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections. Determine (a) P(A) (b) P(B nn barC) (c ) P(A uu B) (d) P(A nn barB) (e) P(B nn C) (f) Probability of the event that exactly one of A, B, and C occurs.