Two balls are drawn from an urn containing 2 white, 3 red and 4 black balls one by one without replacement. What is the probability that at least one ball is red?

Options

A. `(7)/(12)`
B. `(5)/(12)`
C. `(2)/(3)`
D. `(5)/(8)`

Answer

A

Explanation

Let A be the event of not getting a red ball in first draw and B be the event of not getting a red ball in second draw.
`therefore` Required probability
=Probability that at least one ball is red
=1-Probability that none is red
`=1-P(A " and " B)=1-P(A cap B)`
`=1-P(A)P(B//A)=1-(2)/(3)xx(5)/(8)=(7)/(12)`