Question

Three athletes A, B and C participate in a race competetion. The probability of winning A and B is twice of winning C. Then the probability that the race win by A or B, is

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

Answer 1

Answer: (C)

$\frac { 4 } { 5 }$

Answer 2

$P ( A ) = P ( B ) = 2 P ( C )$

$P ( A ) + P ( B ) + P ( C ) = 1$ $\Rightarrow P ( C ) = \frac { 1 } { 5 }$ and $P ( A ) = P ( B ) = \frac { 2 } { 5 }$

Hence $P ( A \cup B ) = P ( A ) + P ( B ) = \frac { 2 } { 5 } + \frac { 2 } { 5 } = \frac { 4 } { 5 }$