Question

Suppose emerson loses 47​% of all chess games. ​(a) what is the probability that emerson loses two chess games in a​ row? (b) what is the probability that emerson loses three chess games in a​ row? assume that each game played is independent of the rest.

Answer 1

From the information given;

P(loss) = 47% = 0.47

Since each game played is independent of the next one, probability of  losing is the same in each play.

Now,
P(losing two games in a row) = P(loss 1 and loss 2) = P(loss 1)*P(loss 2) = P(loss)^2 = 0.47^2 = 0.2209

P(losing 5 games in row) = P(loss)^5 = 0.47^2 = 0.0229