Question

On the tosses of two fair dice. What is the conditional probability that the sum of the two dice will be 8 given that the sum is greater than 7

Answer 1

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Let A be the event that the sum is 7 and let B be the event that the sum is odd. So,

A:(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

and

B:1,2),(1,4),(1,6),(2,1),(2,3),(2,5),-----(6,1),(6,3),(6,5)

and

A∩B:(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Now, there are 36 outcomes in all in tossing 2 fair dice. Hence, P(A)=6/36=1/6 .

P(B)=18/36=1/2 and P(A∩B)=6/36=1/6.

So, P(A/B)=P(A∩B)/P(B)=1/3.

Lastly, there are 6 cases where the outcomes of two dice are same viz (1,1),(2,2),(3,3),(4,4),(5,5) and (6,6). So, the required probability is 6/36 = 1/6.