MAT Exam 2021 Paper

Concept:Total probability of all possible outcomes in a competition is 1.Use the given ratio between the winning probabilities of $A$, $B$ and $C$.Explanation:Let the probability that $C$ wins be $p$.Since $B$ wins twice as often as $C$, $P(B) = 2p$.Since $A$ wins twice as often as $B$, $P(A) = 2(2p) = 4p$.The sum of all winning probabilities must equal 1.$p + 2p + 4p = 1$$7p = 1$$p = \frac{1}{7}$Therefore, $P(A) = 4p = \frac{4}{7}$.The probability that $A$ loses means $A$ does not win.$P(\text{A loses}) = 1 - P(\text{A wins})$$= 1 - \frac{4}{7} = \frac{3}{7}$.Answer:$\frac{3}{7}$, which is Option D.