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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 none of them will win
- a)5/12
- b)7/12
- c)1/12
- d)none
Correct answer is option 'B'. 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:
To find the probability that none of the horses will win, we need to find the probability that both horses will lose.
Let P(A) be the probability of horse A winning and P(B) be the probability of horse B winning.
The probability of both horses losing is given by:
P(¬A ∧ ¬B) = P(¬A) × P(¬B)
where ¬A means "not A" or "A losing" and similarly for ¬B.
Given that P(A) = 1/6 and P(B) = 1/4, we can calculate P(¬A) and P(¬B) as follows:
P(¬A) = 1 - P(A) = 1 - 1/6 = 5/6
P(¬B) = 1 - P(B) = 1 - 1/4 = 3/4
Therefore, the probability of both horses losing is:
P(¬A ∧ ¬B) = P(¬A) × P(¬B) = (5/6) × (3/4) = 15/24 = 5/8
But we need to find the probability that none of the horses will win, which is the same as the probability that both horses will lose. Therefore, the answer is:
P(¬A ∧ ¬B) = 5/8 = 7/12 (option 'B')
Hence, the correct answer is option 'B'.
To find the probability that none of the horses will win, we need to find the probability that both horses will lose.
Let P(A) be the probability of horse A winning and P(B) be the probability of horse B winning.
The probability of both horses losing is given by:
P(¬A ∧ ¬B) = P(¬A) × P(¬B)
where ¬A means "not A" or "A losing" and similarly for ¬B.
Given that P(A) = 1/6 and P(B) = 1/4, we can calculate P(¬A) and P(¬B) as follows:
P(¬A) = 1 - P(A) = 1 - 1/6 = 5/6
P(¬B) = 1 - P(B) = 1 - 1/4 = 3/4
Therefore, the probability of both horses losing is:
P(¬A ∧ ¬B) = P(¬A) × P(¬B) = (5/6) × (3/4) = 15/24 = 5/8
But we need to find the probability that none of the horses will win, which is the same as the probability that both horses will lose. Therefore, the answer is:
P(¬A ∧ ¬B) = 5/8 = 7/12 (option 'B')
Hence, the correct answer is option 'B'.
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Community Answer
If the probability of a horse A winning a race is 1/6 and the probabil...
1-(1/6+1/4)=1-(5/12)=7/12
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