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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
- a)3/5
- b)1/5
- c)2/5
- d)4/5
Correct answer is option 'C'. Can you explain this answer?
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Probability of selecting the winning horse:
To find the probability that Mr. A selected the winning horse, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
There are 5 horses in the race. Mr. A selects 2 horses at random. The total number of possible outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of horses and r is the number of horses selected by Mr. A.
In this case, n = 5 and r = 2.
So, the total number of outcomes is:
5C2 = 5! / (2!(5-2)!) = 10.
Favorable outcomes:
To determine the number of favorable outcomes, we need to consider the cases where Mr. A selects the winning horse.
There are 5 horses in the race, and only 1 of them can be the winner. Mr. A selects 2 horses at random, so there are 2 possible scenarios where he selects the winning horse:
1. He selects the winning horse as one of his choices.
2. He selects both the winning horse and another horse.
Scenario 1:
The probability of selecting the winning horse as one of his choices is given by:
P(Selecting winning horse) = 1/5.
Once Mr. A selects the winning horse, he can choose any other horse for his second choice. So, the number of outcomes in this scenario is:
Number of outcomes = 1 * 4 = 4.
Scenario 2:
The probability of selecting both the winning horse and another horse is given by:
P(Selecting winning horse and another horse) = P(Selecting winning horse) * P(Selecting another horse) = (1/5) * (4/4) = 1/5.
In this case, Mr. A has only one choice for his second selection, which is any of the remaining 4 horses. So, the number of outcomes in this scenario is:
Number of outcomes = 1 * 1 = 1.
Total number of favorable outcomes:
The total number of favorable outcomes is the sum of the outcomes from both scenarios:
Total number of favorable outcomes = 4 + 1 = 5.
Probability:
The probability that Mr. A selected the winning horse is given by:
P(Selecting winning horse) = Number of favorable outcomes / Total number of outcomes = 5 / 10 = 1/2.
Hence, the correct answer is option 'C' (2/5).
To find the probability that Mr. A selected the winning horse, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
There are 5 horses in the race. Mr. A selects 2 horses at random. The total number of possible outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of horses and r is the number of horses selected by Mr. A.
In this case, n = 5 and r = 2.
So, the total number of outcomes is:
5C2 = 5! / (2!(5-2)!) = 10.
Favorable outcomes:
To determine the number of favorable outcomes, we need to consider the cases where Mr. A selects the winning horse.
There are 5 horses in the race, and only 1 of them can be the winner. Mr. A selects 2 horses at random, so there are 2 possible scenarios where he selects the winning horse:
1. He selects the winning horse as one of his choices.
2. He selects both the winning horse and another horse.
Scenario 1:
The probability of selecting the winning horse as one of his choices is given by:
P(Selecting winning horse) = 1/5.
Once Mr. A selects the winning horse, he can choose any other horse for his second choice. So, the number of outcomes in this scenario is:
Number of outcomes = 1 * 4 = 4.
Scenario 2:
The probability of selecting both the winning horse and another horse is given by:
P(Selecting winning horse and another horse) = P(Selecting winning horse) * P(Selecting another horse) = (1/5) * (4/4) = 1/5.
In this case, Mr. A has only one choice for his second selection, which is any of the remaining 4 horses. So, the number of outcomes in this scenario is:
Number of outcomes = 1 * 1 = 1.
Total number of favorable outcomes:
The total number of favorable outcomes is the sum of the outcomes from both scenarios:
Total number of favorable outcomes = 4 + 1 = 5.
Probability:
The probability that Mr. A selected the winning horse is given by:
P(Selecting winning horse) = Number of favorable outcomes / Total number of outcomes = 5 / 10 = 1/2.
Hence, the correct answer is option 'C' (2/5).
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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 isa)3/5b)1/5c)2/5d)4/5Correct answer is option 'C'. Can you explain this answer?
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