Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is?

Correct option is C. 25/32
Let persons be A, B, C, D
P(A)=1/2, P(A⁻)=1-1/2=1/2
P(B)=1/3, P(B⁻)=1-1/3=2/3
P(C)=1/4, P(C⁻)=1-1/4=3/4
P(D)=1/8, P(D⁻)=1-1/8=7/8
P(Hit) = 1 - P(none of them hits) = 1 - P(A⁻∩B⁻∩C⁻∩D⁻) = 1 - P(A⁻)⋅P(B⁻)⋅P(C⁻)⋅P(D⁻) = 1 - (1/2)⋅(2/3)⋅(3/4)⋅(7/8) = 25/32.