CUET UG 2025 — General Test Quantitative Reasoning

A speaks the truth in 70% of cases, so A lies in 30% of cases.

B lies in 40% of cases, so B speaks the truth in 60% of cases.

Therefore:

• P(A tells truth) = $\frac{7}{10}$107​
• P(A lies) = $\frac{3}{10}$103​
• P(B tells truth) = $\frac{3}{5}$53​
• P(B lies) = $\frac{2}{5}$52​

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For A and B to say the same thing while describing a single event, either both tell the truth or both lie.

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P(Both tell truth) = P(A tells truth) × P(B tells truth)

$$= \frac{7}{10} \times \frac{3}{5}$$=107​×53​

$$= \frac{21}{50}$$=5021​

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P(Both lie) = P(A lies) × P(B lies)

$$= \frac{3}{10} \times \frac{2}{5}$$=103​×52​

$$= \frac{6}{50}$$=506​

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P(They say the same thing) = P(Both tell truth) + P(Both lie)

$$= \frac{21}{50} + \frac{6}{50}$$=5021​+506​

$$= \frac{27}{50}$$=5027​

Therefore, the probability that they will say the same thing is $\frac{27}{50}$5027​.