CUET UG 2025 — Mathematics Algebra

A speaks truth in 75% of cases, which is $\dfrac{3}{4}$43​

B speaks truth in 80% of cases, which is $\dfrac{4}{5}$54​

Therefore:

A lies in 25% of cases, which is $\dfrac{1}{4}$41​

B lies in 20% of cases, which is $\dfrac{1}{5}$51​

---

A and B contradict each other when one tells the truth and the other lies.

This can happen in two ways:

Case 1: A speaks truth and B lies

Case 2: A lies and B speaks truth

---

For Case 1 (A speaks truth and B lies):

P(A speaks truth and B lies) = $\dfrac{3}{4} \times \dfrac{1}{5}$43​×51​

$$= \dfrac{3}{20}$$=203​

---

For Case 2 (A lies and B speaks truth):

P(A lies and B speaks truth) = $\dfrac{1}{4} \times \dfrac{4}{5}$41​×54​

$$= \dfrac{4}{20}$$=204​

---

Total probability of contradiction:

P(contradiction) = $\dfrac{3}{20} + \dfrac{4}{20}$203​+204​

$$= \dfrac{7}{20}$$=207​

Therefore, the probability that they contradict each other is $\dfrac{7}{20}$207​