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Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is-
[AIEEE 2003]
- a)2/5
- b)4/5
- c)3/5
- d)1/5
Correct answer is option 'A'. Can you explain this answer?
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Five horses are in a race. Mr. A selects two of the horses at random a...
Let H1H2H3H4 B be the horses in which B is the winning horse.
Required probability
Required probability
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Five horses are in a race. Mr. A selects two of the horses at random a...
To solve this problem, we can use the concept of conditional probability. Let's break down the problem step by step:
Step 1: Find the total number of ways to select two horses out of five.
The total number of ways to select two horses out of five is given by the combination formula:
C(5, 2) = 5!/((5-2)! * 2!) = 10
Step 2: Find the number of ways to select two horses such that one of them is the winning horse.
Since there is only one winning horse out of five, we can select it in 1 way. The other horse can be any of the remaining four horses, so we have 4 choices.
Step 3: Calculate the probability of selecting the winning horse.
The probability of an event is given by the ratio of favorable outcomes to total outcomes. In this case, the favorable outcomes are the number of ways to select two horses such that one of them is the winning horse, which is 4. The total outcomes are the total number of ways to select two horses out of five, which is 10.
Therefore, the probability is 4/10, which simplifies to 2/5.
Hence, the probability that Mr. A selected the winning horse is 2/5, which corresponds to option A.
Step 1: Find the total number of ways to select two horses out of five.
The total number of ways to select two horses out of five is given by the combination formula:
C(5, 2) = 5!/((5-2)! * 2!) = 10
Step 2: Find the number of ways to select two horses such that one of them is the winning horse.
Since there is only one winning horse out of five, we can select it in 1 way. The other horse can be any of the remaining four horses, so we have 4 choices.
Step 3: Calculate the probability of selecting the winning horse.
The probability of an event is given by the ratio of favorable outcomes to total outcomes. In this case, the favorable outcomes are the number of ways to select two horses such that one of them is the winning horse, which is 4. The total outcomes are the total number of ways to select two horses out of five, which is 10.
Therefore, the probability is 4/10, which simplifies to 2/5.
Hence, the probability that Mr. A selected the winning horse is 2/5, which corresponds to option A.
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Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is-[AIEEE 2003]a)2/5b)4/5c)3/5d)1/5Correct answer is option 'A'. Can you explain this answer?
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