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If the probability of a horse A winning a race is 1/6 and the probability of a horse B winning the same race is 1/4 , what is the probability that one of the horses will win
- a)5/12
- b)7/12
- c)1/12
- d)none
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the probability of a horse A winning a race is 1/6 and the probabil...
Solution:
Given that the probability of horse A winning a race is 1/6 and the probability of horse B winning the same race is 1/4.
To find: The probability that one of the horses will win.
Let P(A) be the probability of horse A winning the race and P(B) be the probability of horse B winning the race.
We need to find P(A ∪ B), which is the probability of either horse A or horse B winning the race.
Formula Used:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where P(A ∩ B) is the probability of both horse A and horse B winning the race.
Calculation:
Given P(A) = 1/6 and P(B) = 1/4
P(A ∩ B) = P(A) × P(B) = (1/6) × (1/4) = 1/24
Now, using the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= (1/6) + (1/4) - (1/24)
= (4/24) + (6/24) - (1/24)
= 9/24
= 3/8
Therefore, the probability that one of the horses will win is 3/8, which is not one of the options given. However, we can simplify this fraction to get the answer in one of the given options:
3/8 = (3/8) ÷ (1/3)
= (3/8) × (3/1)
= 9/24
= 5/12
Therefore, the correct answer is option A) 5/12.
Given that the probability of horse A winning a race is 1/6 and the probability of horse B winning the same race is 1/4.
To find: The probability that one of the horses will win.
Let P(A) be the probability of horse A winning the race and P(B) be the probability of horse B winning the race.
We need to find P(A ∪ B), which is the probability of either horse A or horse B winning the race.
Formula Used:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where P(A ∩ B) is the probability of both horse A and horse B winning the race.
Calculation:
Given P(A) = 1/6 and P(B) = 1/4
P(A ∩ B) = P(A) × P(B) = (1/6) × (1/4) = 1/24
Now, using the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= (1/6) + (1/4) - (1/24)
= (4/24) + (6/24) - (1/24)
= 9/24
= 3/8
Therefore, the probability that one of the horses will win is 3/8, which is not one of the options given. However, we can simplify this fraction to get the answer in one of the given options:
3/8 = (3/8) ÷ (1/3)
= (3/8) × (3/1)
= 9/24
= 5/12
Therefore, the correct answer is option A) 5/12.
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Community Answer
If the probability of a horse A winning a race is 1/6 and the probabil...
1/6+1/4=10/24=5/12
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