There are two urns `Aa n dB` . Urn `A` contains 5 red, 3 blue and 2 white balls, urn `B` contains 4 red, 3 blue, and 3 white balls. An urn is chosen at random and a ball is drawn. Probability that the ball drawn is red is a. `9//10` b. `1//2` c. `11//20` d. `9//20`

Options

A. `9//10`
B. `1//2`
C. `11//20`
D. `9//20`

Answer

D

Explanation

Let A nad B, respectively, be the events that urn A and urn B are selected.Let R be the event that the selected ball is red. Since tue urn is chosen at random, Therefore,
`P(A) =P(B)=1/2`
`and P(R)=P(A)P(R//A)+P(B)P(R//B)`
`=1/2xx5/10xx4/10=9/20`