question_answer

There are two bags A and B. Bag A contains 6 red balls and 10 green balls and bag B contains 4 red balls and 6 green balls. One bag is selected at random. From the selected bag one ball is drawn at random. What is the probability that the ball drawn is red?                                                                                                                  [SBI (SO) 2016]

A) \[\frac{27}{80}\]                                   

B) \[\frac{31}{80}\]

C) \[\frac{39}{80}\]                                   

D) \[\frac{20}{80}\]

E) \[\frac{33}{80}\]

Correct Answer: B

Solution :

Probability of drawing one red from bag \[A=\frac{6}{16}\]

Probability of drawing one red from bag \[B=\frac{4}{10}\]

Probability to select one bag \[=\frac{1}{2}\]

\[\therefore \] Required probably \[=\frac{1}{2}\left( \frac{6}{16}+\frac{4}{10} \right)=\frac{31}{80}\]