13.10     A black and a red dice are rolled. 

               (b) Find the conditional probability of obtaining the sum 8,  given that the red die resulted in a number less than 4.

Answers (1)

 A black and a red dice are rolled.

Total outcomes =6^{2}=36

Let the  A be event obtaining a sum 8  and B be a event thatthat the red die resulted in a number less than 4.

A=\left \{ 26,35,53,44,62, \right \}

n(A)=5

Red dice is rolled after black dice.

B=\left \{ 11,12,13,21,22,23,31,32,33,41,42,43,51,52,53,61,62,63 \right \}

n(B)=18

A\cap B=\left \{ 53,62 \right \}

n(A\cap B)=2

P(A\cap B)=\frac{2}{36}

P( B)=\frac{18}{36}

P(A| B)=\frac{P(A\cap B)}{P(B)}

P(A| B)=\frac{\frac{2}{36}}{\frac{18}{36}}=\frac{2}{18}=\frac{1}{9}

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