A boy can throw a ball in a box with a probability of 1/4. What is the probability that at least one ball falls in the box if he has 4 throws?

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.