Question

The probability of selecting a green ball from a bag is 1 out of 8, assuming there are 8 balls in the bag. If you select 3 balls, what is the probability of at least one of them being green?

Answer 1

3/8 = 0.375

Explanation:

Probability of selecting a green ball =
`(1)/(8)`

Probability of not selecting a green ball = 1 - Probability of selecting a green ball

So,

Probability of not selecting a green ball =
`1-(1)/(8)=(7)/(8)`

Probability of "atleast 1" is complement of Probability of "None".

Therefore,

The probability of at least one of them being green is complement of probability that none of the balls is green.

Probability of selecting first ball which is not green =
`(7)/(8)`

After selecting the first ball, there are 7 balls in the bag with 1 green ball and 6 non-green balls. So, probability of selecting second non-green ball =
`(6)/(7)`

Similarly, probability of selecting 3rd non-green ball =
`(5)/(6)`

Hence,

The probability that none of the balls would be green =
`(7)/(8) * (6)/(7) * (5)/(6) = (5)/(8)`

Probability that atleast one of the balls would be green = 1 - probability that none of the balls would be green

Probability that atleast one of the balls would be green = 1 -
`(5)/(8) = (3)/(8) = 0.375`