Q. 175.0( 2 Votes )

A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that

i. Both are white

ii. Both are black

iii. One is white and one is black

Answer :

Given:


Bag A contains 4 white balls and 2 black balls


Bag B contains 3 white balls and 5 black balls


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


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:


i. P(DWW) = P(Both are white)


ii. P(DBB) = P(Both are black)


iii. P(DWB) = P(One drawn is white and other is black)


P(DWW) = P(Both are White)


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





P(DBB) = P(Both balls are black)


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





P(DWB) = P(One ball drawn is white and other is black)


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





.


The required probabilities are .


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