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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?
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.
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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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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 wina)5/12b)7/12c)1/12d)noneCorrect answer is option 'A'. Can you explain this answer?
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