A bag contains 5 white and 3 black balls...

A bag contains 5 white and 3 black balls. Four balls are successively drawn out without replacement. What is the probability that they are alternately of different colours?

`1/196`

`2/7`

`13/56`

`1/7`

Text Solution

Verified by Experts

The correct Answer is:

Required probability
`=P(WBWB)+P(BWBW)`
`=((.^(5)C_(1)xx.^(3)C_(1)xx.^(4)C_(1)xx.^(2)C_(1))/(.^(8)C_(1)xx.^(7)C_(1)xx.^(6)C_(1)xx.^(5)C_(1)))`
`+((.^(3)C_(1)xx.^(5)C_(1)xx.^(2)C_(1)xx.^(4)C_(1))/(.^(8)C_(1)xx.^(7)C_(1)xx.^(6)C_(1)xx.^(5)C_(1)))`
`=1/14+1/14=1/7`

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