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  • A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.

A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.

 

Answers (1)

Given-

 A and B throw a pair of dice alternately.

A wins if he gets a total of 6

And B wins if she gets a total of 7

Therefore,

 A = {(2,4), (1,5), (5,1), (4,2), (3,3)}  and
B = {(2,5), (1,6), (6,1), (5,2), (3,4), (4,3)}

Let  P(B)  be the probability that A wins in a throw \Rightarrow P(A)=\frac{5}{36}$
And P(B) be the probability that B wins in a throw \Rightarrow P(B)=\frac{1}{6}$
\therefore$  The probability of A winning the game in the third row

\rightarrow$ $P(\bar{A}) \cdot P(\bar{B}) \cdot P(A)=\frac{31}{36} \times \frac{5}{6} \times \frac{5}{36}=\frac{775}{216 \times 36}$
=\frac{775}{7776}$

Posted by

infoexpert22

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