Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?
Step-by-Step Solution
Key Concept: The sum of probabilities of all mutually exclusive and exhaustive outcomes of a single experiment is 1. Hence, the probability of the complementary event is $1 - P(\text{given event})$.
1. Let $S$ denote the event that Sangeeta wins the match and $R$ denote the event that Reshma wins the match.
2. Since the match can be won by either Sangeeta or Reshma and there are no other possibilities, the events $S$ and $R$ are mutually exclusive and exhaustive.
3. Therefore, $$P(S) + P(R) = 1.$$
4. Given $P(S) = 0.62$, substitute this value:
$$0.62 + P(R) = 1.$$
5. Solve for $P(R)$:
$$P(R) = 1 - 0.62 = 0.38.$$
6. Hence, the probability that Reshma wins the match is $0.38$.
Correct Answer: 0.38