Two Grand Masters Anand and Karpov, play 3 games of chess. The probability that Anand wins a game is 0.5, looses with probability 0.3 and ties with probability 0.2. If he plays 3 games then the chance that he wins atleast two games, is

Question

Two Grand Masters Anand and Karpov, play 3 games of chess. The probability that Anand wins a game is 0.5, looses with probability 0.3 and ties with probability 0.2. If he plays 3 games then the chance that he wins atleast two games, is (A) 0.3 (B) 0.4 (C) 0.6 (D) 0.5

Tardigrade Admin · Accepted Answer

P (T or L) = 0.5 = P (E) say P (W W E or W E W or E W W or W W W) =4 ⋅ (5/10) ⋅ (5/10) ⋅ (5/10)=(1/2)

Q. Two Grand Masters Anand and Karpov, play 3 games of chess. The probability that Anand wins a game is 0.5, looses with probability 0.3 and ties with probability 0.2. If he plays 3 games then the chance that he wins atleast two games, is

0.3

0.4

0.6

0.5

P (T or L) = 0.5 = P (E) say
P (W W E or W E W or E W W or W W W)
$= 4 \cdot \frac{5}{10} \cdot \frac{5}{10} \cdot \frac{5}{10} = \frac{1}{2}$

Q. Two Grand Masters Anand and Karpov, play 3 games of chess. The probability that Anand wins a game is 0.5, looses with probability 0.3 and ties with probability 0.2. If he plays 3 games then the chance that he wins atleast two games, is

0.3

0.4

0.6

0.5

P (T or L) = 0.5 = P (E) say P (W W E or W E W or E W W or W W W) =4⋅105​⋅105​⋅105​=21​

P (T or L) = 0.5 = P (E) say
P (W W E or W E W or E W W or W W W)
$= 4 \cdot \frac{5}{10} \cdot \frac{5}{10} \cdot \frac{5}{10} = \frac{1}{2}$