Q. 13.5( 4 Votes )

A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.

Answer :

Given:


Bag A contains 6 black balls and 3 white balls


Bag B contains 5 black balls and 4 white balls


It is told that one ball is drawn is drawn from is each bag.


We need to find the probability that the balls are of the same colour.


Let us find the Probability of drawing each colour ball from the bag.


P(B1) = P(drawing black ball from bag A)





P(W1) = P(drawing white ball from bag A)





P(B2) = P(drawing black ball from bag B)





P(W2) = P(drawing white ball from bag B)





We need to find the probability of drawing the same colour balls from two bags


P(S) = P(drawing two balls of same colours) = P(drawing black balls from each bag) + (P(drawing white balls from each bag)


Since drawing a ball is independent for each bag, the probabilities multiply each other.





.


The required probability is .


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