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KCET 2026 Mathematics Solved Paper

Question : 56 of 60

Marks: +1, -0

12 \%

=24 \%

=9 \%

=17 \%

=22 \%

P(A)=P(B)=P(C)=P(D)=1 / 4

P(A \mid L)

Solution:

Concept:

Use Bayes' theorem to find the probability that both parents are left handed, given that the child is left handed.

Explanation:

We need

P(A \mid L)

, the probability of event

A

given

L

By Bayes' theorem,

P(A \mid L) = \frac{P(A) \cdot P(L \mid A)}{P(L)}

Given

P(A) = P(B) = P(C) = P(D) = \frac{1}{4}

Also,

P(L \mid A) = \frac{24}{100}

Find total probability

P(L)

using the law of total probability:

P(L) = \frac{1}{4} \times \frac{24}{100} + \frac{1}{4} \times \frac{9}{100} + \frac{1}{4} \times \frac{17}{100} + \frac{1}{4} \times \frac{22}{100}

Take

\frac{1}{4}

common:

P(L) = \frac{1}{4} \times \frac{24 + 9 + 17 + 22}{100} = \frac{1}{4} \times \frac{72}{100}

Now substitute into Bayes' formula:

P(A \mid L) = \frac{\frac{1}{4} \times \frac{24}{100}}{\frac{1}{4} \times \frac{72}{100}} = \frac{24}{72} = \frac{1}{3}

Answer:

\frac{1}{3}

, which is option C.

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