A bag contains `5` red and `3` blue balls. If `3` balls are drawn at random without replacement, then the probability of getting exactly one red ball is

Options

A. a) `(15)/(29)`
B. b) `(15)/(56)`
C. c) `(45)/(196)`
D. d) `(15)/(392)`

Answer

Explanation

Probability of drawing exactly one red ball


`P_R=`red ball, `P_B=`blue ball


`=P_R*P_B*P_B+P_B*P_R*P_B+P_B*P_B*P_R`


`=5/8*3/7*2/6+3/8*5/7*2/6+3/8*2/7*5/6`


`=15/(4*7*6)+ 15/(4*7*6)+ 15/(4*7*6)`


`=(3*15)/(4*7*6)=15/56`


Hence, correct option is b)