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In a certain town, 40% persons have brown hair, 25% have brown eyes, and 15% have both. If a person selected at random has brown hair, the chance that a person selected at random with brown hair is with brown eyes
  • a)
    3/8
  • b)
    1/3
  • c)
    3/20
  • d)
    2/3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a certain town, 40%persons have brown hair, 25%have brown eyes, and...
Solution:

Given that 40% of persons have brown hair, 25% have brown eyes, and 15% have both.

Let A be the event that a person has brown hair, and B be the event that a person has brown eyes.

Then, P(A) = 0.40, P(B) = 0.25, and P(A ∩ B) = 0.15.

We are asked to find the probability that a person selected at random with brown hair is also with brown eyes, i.e., P(B|A).

Using Bayes' theorem, we have:

P(B|A) = P(A ∩ B) / P(A)

Substituting the given values, we get:

P(B|A) = 0.15 / 0.40

Simplifying, we get:

P(B|A) = 3/8

Therefore, the answer is option (A).
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Community Answer
In a certain town, 40%persons have brown hair, 25%have brown eyes, and...
Let A be the event that the people have brown hair and B be the event that the people have brown eyes.

Therefore, P(A) = 40% = 40/100

P(B) = 25% = 25/100

P(A∩B) = 15% = 15/100

Hence, the required probability = P(B/A)

P(B/A) = P(A∩B)/P(B)

P(B/A) = (15/100)/(40/100)

P(B/A) = 15/40

P(B/A) = 3/8
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