The probability that A hits a target is \(\frac{1}{4}\), and the probability that B hits the target is \(\frac{2}{5}\). Both shoot at the target, what is the probability that at least one of them hits the target, i.e., that A or B (or both) hit the target?

The correct answer is Option 1.

Key Points

• Let the probability that A hits the target be $P(A) = \frac{1}{4}$ .
• Let the probability that B hits the target be $P(B) = \frac{2}{5}$ .
• The probability that neither A nor B hits the target is the product of their individual probabilities of missing the target.
• The probability that A misses the target is $1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$ .
• The probability that B misses the target is $1 - P(B) = 1 - \frac{2}{5} = \frac{3}{5}$ .
• The probability that neither hits the target is $\left(\frac{3}{4}\right) \times \left(\frac{3}{5}\right) = \frac{9}{20}$ .
• The probability that at least one of them hits the target is $1 - \frac{9}{20} = \frac{11}{20}$ .

Additional Information

• This problem involves the concept of complementary probability, which is useful when calculating the probability of at least one event occurring.In probability theory, the complement rule is used to determine the probability of an event not occurring.
• Option 1 is indeed correct as the final probability calculation matches the probability required.