Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

59. Two players, [tex]A[/tex] and [tex]B[/tex], play a tennis match. If the probability of winning the match by [tex]A[/tex] is [tex]\frac{1}{3}[/tex], what is the probability of winning the match by [tex]B[/tex]?

(Note: The original text included non-English characters that were not part of the question and were thus removed for clarity.)


Sagot :

Certainly! Let's solve the problem step-by-step.

1. Given Information:
- The probability of player A winning the match is [tex]\(\frac{1}{3}\)[/tex].

2. Understanding Probabilities:
- In probability, the sum of the probabilities of all mutually exclusive outcomes must equal 1.
- For this problem, there are only two possible outcomes: either player A wins or player B wins.

3. Setting Up the Equation:
- Let [tex]\(P(A)\)[/tex] be the probability that player A wins the match.
- Let [tex]\(P(B)\)[/tex] be the probability that player B wins the match.
- According to the problem, [tex]\(P(A) = \frac{1}{3}\)[/tex].

4. Calculating the Probability for Player B:
- The sum of the probabilities for player A and player B winning is 1.
- Therefore, we can write the equation:
[tex]\[ P(A) + P(B) = 1 \][/tex]
- We substitute the value of [tex]\(P(A)\)[/tex] from the given information:
[tex]\[ \frac{1}{3} + P(B) = 1 \][/tex]

5. Solving for [tex]\(P(B)\)[/tex]:
- To find [tex]\(P(B)\)[/tex], we solve the equation for [tex]\(P(B)\)[/tex]:
[tex]\[ P(B) = 1 - \frac{1}{3} \][/tex]

6. Simplifying the Expression:
- Perform the subtraction:
[tex]\[ P(B) = \frac{3}{3} - \frac{1}{3} = \frac{2}{3} \][/tex]

7. Result:
- Therefore, the probability that player B wins the match is [tex]\(\frac{2}{3}\)[/tex].

So, the probability of winning the match by player B is [tex]\[\frac{2}{3}\][/tex] or approximately 0.6666666666666667.