# The probability of picking a red ball from a box is 0.25. When 4 balls are picked from the box what is the probability of picking a red ball.

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### 1 Answer

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` .