Question

Bob and Meena play a two-person game which is won by the first person to accumulate at least 10 points. On each turn, there is a $\frac{2}{5}$ probability that Bob will get two points and Meena will lose one point. If that doesn't happen, then Meena gets two points and Bob loses a point. Meena is now ahead 9 to 6. What is the probability that Meena will win?

Answer 1

Answer:

The probability that Meena wins is 21/25

Step-by-step explanation:

In order for Meena to win, she needs to win the next turn or the following one, otherwise, she loses. The probability for that is equal to substract from 1 the probability of the complementary event: bob wins in the next 2 turns. Since each turn is independent from the other, we can obtain the probability of Bob winning the next 2 turns by taking the square of the probability of him winning on one turn, hence it is

${\frac{2}{5}}^2 = \frac{4}{25}$

Thus, the probability for Meena to win is 1-4/25 = 21/25.