Question

In the game A and B had to play, the probability of A's winning is $\frac{2}{5}$ , if he had lost the previous game and $\frac{3}{5}$ if he had won the previous game. In the middle of series of games, the probability of A's winning two games in succession is

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{4}{5}$

Answer 1

Answer: (C)

$\frac{3}{5}$

Case 1: He lost a previous game
P (winning both) $=2/5\ast 3/5$
Case 2: He won the previous game
P(winning both) $=3/5\ast 3/5$
$\Rightarrow P=6/25+9/25=3/5$