The probability that the boy throws the ball in the box is given as 1/4. He is given 4 attempts and we need to find the probability that he will throw the ball in the box at least once.
The condition that he will throw the ball in the box at least once is satisfied if he is able to throw 1, 2, 3 or 4 balls in the box.
He does not succeed if no ball is thrown into the box. The probability of his not being able to throw the ball in the box is 1 – 1/4 = 3/4
Given four attempts the probability that he fails all the four times is (3/4)^4 = 81/256.
Therefore the probability that he can throw the ball in the box at least once is
1 – 81/ 256 = 175/ 256.