CUET UG 2025 — General Test Quantitative Reasoning

The probability of P's selection is $\frac{1}{3}$31​ and the probability of Q's selection is $\frac{2}{7}$72​.

To find the probability that at least one of them will be selected, we use:

P(At least one selected) = 1 - P(Neither selected)

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The probability that P is not selected:

$$P(\text{P not selected}) = 1 - \frac{1}{3}$$P(P not selected)=1−31​

$$= \frac{2}{3}$$=32​

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The probability that Q is not selected:

$$P(\text{Q not selected}) = 1 - \frac{2}{7}$$P(Q not selected)=1−72​

$$= \frac{5}{7}$$=75​

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Since the selections are independent, the probability that neither gets selected:

$$P(\text{Neither selected}) = \frac{2}{3} \times \frac{5}{7}$$P(Neither selected)=32​×75​

$$= \frac{10}{21}$$=2110​

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The probability that at least one gets selected:

$$P(\text{At least one selected}) = 1 - \frac{10}{21}$$P(At least one selected)=1−2110​

$$= \frac{21}{21} - \frac{10}{21}$$=2121​−2110​

$$= \frac{11}{21}$$=2111​

Therefore, the probability that at least one of them will be selected is $\frac{11}{21}$2111​.