Question

Two players, Anand and Vishwa are playing a tennis match. The probability of Vishwa winning the match is 0.75. What is the probability of Anand winning the match?

Options: A $\frac{4}{3}$ B $\frac{2}{4}$ C $\frac{1}{4}$ D $\frac{3}{4}$

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Answer


The correct option is C: $$ \frac{1}{4} $$

Let $E$ represent the event of Vishwa winning the match. Conversely, the event of Anand winning the match would be denoted as (not $E$).

Given: $$ P(E)=\frac{\text{Number of outcomes favorable to } E \text{ }}{\text{Total number of outcomes}} = 0.75 = \frac{3}{4} $$

Since the sum of probabilities of all possible outcomes in a probability distribution always equals 1, we have: $$ P(E) + P(\text{not } E) = 1 $$

Thus, $$ P(\text{not } E) = 1 - P(E) = 1 - \frac{3}{4} = \frac{1}{4} $$

Therefore, the probability of Anand winning the match is: $$ \frac{1}{4} $$


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