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A player is going to play a match either in the morning or in the afternoon or in the evening all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1 and 0.8 according as if the match is played in the morning, afternoon or in the evening respectively. Given that he has won the match, the probability that the match was played in the afternoon is
- a)1/12
- b)1/15
- c)2/27
- d)1/10
- e)1/20
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A player is going to play a match either in the morning or in the afte...
This is the problem of conditional probability, so by Bave’s theorem.
A = the game was played in afternoonB B = player won the game.
A = the game was played in afternoonB B = player won the game.
Most Upvoted Answer
A player is going to play a match either in the morning or in the afte...
This is the problem of conditional probability, so by Bave’s theorem.
A = the game was played in afternoonB B = player won the game.
A = the game was played in afternoonB B = player won the game.
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A player is going to play a match either in the morning or in the afte...
Solution:
Given:
A player is going to play a match either in the morning, afternoon, or in the evening, all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1, and 0.8 according to whether the match is played in the morning, afternoon, or in the evening respectively.
To Find:
Given that he has won the match, the probability that the match was played in the afternoon.
Solution Approach:
Step 1: Find the Probability of Winning the Match:
To find the probability of winning the match, we need to consider the weighted average of the probabilities based on the time of the match.
\[P(\text{winning}) = (0.6 + 0.1 + 0.8) / 3 = 1.5 / 3 = 0.5\]
Step 2: Apply Bayes' Theorem:
Now, we can apply Bayes' Theorem to find the probability that the match was played in the afternoon given that the player has won.
\[P(\text{afternoon}|\text{win}) = P(\text{win}|\text{afternoon}) * P(\text{afternoon}) / P(\text{win})\]
Given:
\[P(\text{win}|\text{afternoon}) = 0.1\]
\[P(\text{afternoon}) = 1/3\]
\[P(\text{win}) = 0.5\]
Substitute the values:
\[P(\text{afternoon}|\text{win}) = 0.1 * (1/3) / 0.5 = 0.1/1.5 = 1/15\]
Therefore, the probability that the match was played in the afternoon given that the player has won is \(1/15\).
Therefore, the correct answer is option B - 1/15.
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