Question

A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B, If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.

Answer 1

Let the event be defined as follows:

E₁=The die shows 1 or 2

E₂=The die shows 3, 4, 5 or 6

E=One of the ball

P(E₁)=2/6=1/3 and P(E₂)=4/6=2/3 drawn is red and another is black

The probability of drawing a red and a black ball from bag A is given by 

`P(E|E_1)=6/10xx4/9+4/10xx6/9=8/15`

The probability of drawing a red and a black ball from bag B is given by

`P(E|E_2)=3/10xx7/9+7/10xx3/9=7/15`

Using the theorem of total probability, we have

`P(E)=P(E_1)P(E|E_1)+P(E_2)P(E|E_2)       `

`=1/3xx8/15+2/3xx7/15       `

`=22/45`