# A Die is Thrown Three Times. Events a and B Are Defined as Below: a : 5 on the First and 6 on the Second Throw. B: 3 Or 4 on the Third Throw. Find the Probability of B, Given that a Has Already Occurred. - Mathematics

A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.

Find the probability of B, given that A has already occurred.

#### Solution

A is an event of getting 5 on the first throw and 6 on the second throw.
Then
A={(5,6,1)  (5,6,2)  (5,6,3)  (5,6,4)  (5,6,5)  (5,6,6)}

Also, B is an event of getting 3 or 4 on the third throw.

AB={(5,6,3), (5,6,4)}

Required probability, P(A|B)=(n(A∩B))/(n(A))=2/6=1/3

Thus, the probability of B, given that A has already occurred is 1/3

Concept: Conditional Probability
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