Moderate Probability Solved QuestionAptitude Discussion

 Q. A bag contains 3 white balls and 2 black balls. Another bag contains 2 white and 4 black balls. A bag and a ball are picked random. The probability that the ball will be white is:
 ✖ A. 7/11 ✖ B. 7/30 ✖ C. 5/11 ✔ D. 7/15

Solution:
Option(D) is correct

The probability of selecting one bag $=\dfrac{1}{2}$

Now, probability of getting a white ball from bag $A$:

$=\dfrac{1}{2}\times \dfrac{3}{5}=\dfrac{3}{10}$

and probability of getting a white ball from bag $B$:

$=\dfrac{1}{2}\times \dfrac{2}{6}=\dfrac{1}{6}$

Hence, Probability that white ball is drawn either first or second bag:

$= 3/10 + 1/6 = 7/15$

(2) Comment(s)

Raj
()

The probability of picking a ball should not have any relation with picking the bag

Joey
()

It sure is related since it has to be picked from one of the two available bags. White ball coming from bag 1 has different probability than white ball coming from bag 2.

In other words, the probability is different when same balls are kept inside one bag only.