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  • A black and a red dice are rolled . (a) Find the conditional probability of obtaining a sum greater than 9 , given that the black die resulted in a 5.

13.10    A black and a red dice are rolled.

                (a)  Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

Answers (1)

best_answer

 A black and a red dice are rolled.

Total outcomes =6^{2}=36

Let the  A be event obtaining a sum greater than 9 and B be a event that the black die resulted in a 5.

A=\left \{ 46,55,56,64,65,66 \right \}

n(A)=6

B=\left \{ 51,52,53,54,55,56 \right \}

n(B)=6

A\cap B=\left \{ 55,56 \right \}

n(A\cap B)=2

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

P( B)=\frac{6}{36}

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

P(A| B)=\frac{\frac{2}{36}}{\frac{6}{36}}=\frac{2}{6}=\frac{1}{3}

Posted by

seema garhwal

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