The probability that A hits a target is 1/4, and the probability that B hits…

Let

• P(A)=14P(A) = \frac{1}{4}P(A)=41​ = probability that A hits the target

• P(B)=25P(B) = \frac{2}{5}P(B)=52​ = probability that B hits the target

Assuming A and B shoot independently, the probability that at least one hits the target is:

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B)P(A∩B)=14×25=110P(A \cap B) = \frac{1}{4} \times \frac{2}{5} = \frac{1}{10}P(A∩B)=41​×52​=101​

Now substitute:

P(A∪B)=14+25−110P(A \cup B) = \frac{1}{4} + \frac{2}{5} - \frac{1}{10}P(A∪B)=41​+52​−101​

Convert to a common denominator (20):

=520+820−220=1120= \frac{5}{20} + \frac{8}{20} - \frac{2}{20} = \frac{11}{20}=205​+208​−202​=2011​

✔ Correct option: D (11/20)