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In a horse race there were 18 horses numbered 1-18. The probability that horse 1 would win is 1/6, that 2 would win is 1/10 and that 3 would win is 1/8.
Assuming that a tie is impossible, find the chance that one of the three will win.
Assuming that a tie is impossible, find the chance that one of the three will win.
- a)47/120
- b)119/120
- c)11/129
- d)1/5
Correct answer is option 'A'. Can you explain this answer?
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In a horse race there were 18 horses numbered 1-18. The probability th...
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In a horse race there were 18 horses numbered 1-18. The probability th...
Probability of Each Horse Winning
To begin with, we are given the probability of each horse winning the race. These are:
- P(Horse 1 wins) = 1/6
- P(Horse 2 wins) = 1/10
- P(Horse 3 wins) = 1/8
Probability of One of the Three Winning
We need to find the probability that one of the three horses (1, 2, or 3) will win the race. To do this, we can use the following formula:
P(1 or 2 or 3 wins) = P(1 wins) + P(2 wins) + P(3 wins) – P(1 and 2 win) – P(1 and 3 win) – P(2 and 3 win) + P(1 and 2 and 3 win)
In this case, we can assume that the probability of any two horses winning the race together is negligible, so we can ignore the terms that involve two horses winning together. We are also given that a tie is impossible, so we do not need to consider that possibility either.
Using the above formula, we can calculate the probability of one of the three horses winning as follows:
P(1 or 2 or 3 wins) = 1/6 + 1/10 + 1/8 = 47/120
Therefore, the answer is option A, 47/120.
To begin with, we are given the probability of each horse winning the race. These are:
- P(Horse 1 wins) = 1/6
- P(Horse 2 wins) = 1/10
- P(Horse 3 wins) = 1/8
Probability of One of the Three Winning
We need to find the probability that one of the three horses (1, 2, or 3) will win the race. To do this, we can use the following formula:
P(1 or 2 or 3 wins) = P(1 wins) + P(2 wins) + P(3 wins) – P(1 and 2 win) – P(1 and 3 win) – P(2 and 3 win) + P(1 and 2 and 3 win)
In this case, we can assume that the probability of any two horses winning the race together is negligible, so we can ignore the terms that involve two horses winning together. We are also given that a tie is impossible, so we do not need to consider that possibility either.
Using the above formula, we can calculate the probability of one of the three horses winning as follows:
P(1 or 2 or 3 wins) = 1/6 + 1/10 + 1/8 = 47/120
Therefore, the answer is option A, 47/120.
Community Answer
In a horse race there were 18 horses numbered 1-18. The probability th...
1/6 + 1/10 + 1/8 = 47/120
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