CUET UG 2025 — Mathematics Algebra

We need to find the probability that the target is hit, meaning at least one of A or B hits it.

$$P(A \text{ hits}) = \dfrac{1}{5}$$P(A hits)=51​

$$P(B \text{ hits}) = \dfrac{2}{3}$$P(B hits)=32​

Instead of calculating each case separately (only A hits, only B hits, both hit), we use a faster approach:

$$P(\text{at least one hits}) = 1 - P(\text{nobody hits})$$P(at least one hits)=1−P(nobody hits)

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$$P(A \text{ misses}) = 1 - \dfrac{1}{5} = \dfrac{4}{5}$$P(A misses)=1−51​=54​

$$P(B \text{ misses}) = 1 - \dfrac{2}{3} = \dfrac{1}{3}$$P(B misses)=1−32​=31​

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Since A and B shoot independently, we can multiply their miss probabilities to get the probability that both miss:

$$P(\text{both miss}) = \dfrac{4}{5} \times \dfrac{1}{3} = \dfrac{4}{15}$$P(both miss)=54​×31​=154​

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Using the complement:

$$P(\text{target is hit}) = 1 - \dfrac{4}{15} = \dfrac{15 - 4}{15} = \boxed{\dfrac{11}{15}}$$P(target is hit)=1−154​=1515−4​=1511​​