# When two dice are rolled what is the probability that the sum of the two numbers is even given that the second die has a even number.

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### 2 Answers

Two dice are rolled. It is known that the sum of the number that turns up in the two dice is even and that the second die is even. The first die can take on 6 different values. Of these three values make the sum even given that the second die has a even number. The probability of an event is the number of outcomes favorable to the event divided by the total number of outcomes. Here, the total number of outcomes is 6 and the number of favorable outcomes is 3. The probability is 3/6 = 1/2.

**The required probability is 1/2**.

A= Event that sum of the numbers on faces of die is even.

={(1,1),(1,3),(1,5),(2,2),(2,4),........,(6,6)}

n(A)=18

`P(A)=18/36`

B= Event that a number of the face of second die is even.

={(1,2),(1,4),(1,6),(2,2),...........,(6,6)}

n(B)=18

`P(B)=18/36`

`AnnB=` {(2,2),(2,4),(2,6),..........,(6,6)}

`n(AnnB)=9`

`P(AnnB)=9/36`

Thus

`P(A//B)=(P(AnnB))/(P(B))=(9//36)/(18//36)`

`=1/2`

Thus the probability that the sum of the two numbers is even given that the second die has a even number is 1/2.