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One bag contains 4 white and 2 black balls. Another contains 3 white and 5 black balls. one ball is drawn from each bag. what is probability that both are white?

What my approach is i am trying to mix these two bags and hence i have now total 14 balls. Now i will take 2 balls out of this new bag. but i am not getting right answer.

I want to know whether this approach is wrong or there is any other approach.

Thanks

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  • $\begingroup$ Your approach allows the possibility that both of the drawn balls were originally in the same bag. The problem doesn't allow that possibility. $\endgroup$
    – Andreas Blass
    Dec 15, 2016 at 4:50
  • $\begingroup$ Since the question says "one ball is drawn from each bag", mixing them doesn't seem to be right. By mixing you are now even getting cases where both balls are drawn from the same bag $\endgroup$
    – Serenity
    Dec 15, 2016 at 4:52
  • $\begingroup$ @ shreyas s this is my question why it does not seem right to mix two bags. what is the difference beetween taking out balls from the same bag and two separate bags $\endgroup$
    – Neeraj Sharma
    Dec 15, 2016 at 5:07

1 Answer 1

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Bag 1 contains $4$ white and $2$ black balls.
Bag 2 contains $3$ white and $5$ black balls.
We know that the probability = No.of favorable outcomes/Total No.of outcomes
Hence, $P_1 = \text {Probability of selecting white ball from bag 1} = \frac {4}{4+2} =\frac {2}{3} $
and $P_2 = \text {Probability of selecting white ball from bag 2} =\frac {3}{3+5} =\frac {3}{8} $.

As both the events are independent, the probability of occurrence of both the events is $$P_{req} =P_1\times P_2 =\frac {2}{3}\times \frac {3}{8} = \frac {1}{4}.$$

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