When a ball is picked from the box the probability that it is red is given to be 0.25. The probability that has to be determined is that of picking a red ball when 4 balls are picked from the box. Intuitively the answer may seem to be 1, but that is not the case.
It is not given that only one of the balls picked must be red in color, the number of balls picked that are red in color can be 1, 2, 3 or 4. The only case that is not allowed is none of the balls picked being red in color.
The probability of picking a red ball from the box is 0.25. This gives the probability of not picking a red ball as 1 - 0.25 = 0.75. The probability that all the 4 balls picked are not red is 0.75^4 = `81/256`
The probability that a red ball is picked is given by `1 - 81/256 = 175/256`
The required probability of picking a red ball when 4 balls are picked from the box is `175/256` .