Q. 325.0( 3 Votes )

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting.

i. 2 red balls

ii. 2 blue balls

iii. One red and one blue ball

Answer :

Given:


Urn contains 7 red and 4 blue balls


It is told that two balls are drawn with replacement


Let us find the probability of drawing each marble from bag


P(B) = P(Drawing a Blue Ball)





P(R) = P(Drawing a Red Ball)





We need to find the probability that the balls drawn:


i. Both in red colour


ii. Both in blue colour


iii. One red and one blue


P(SRR) = P(drawing Two red colour balls)


Since drawing a ball is an independent event, the probabilities multiply each other.





P(SBB) = P(drawing two blue colour balls)


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





P(Sany) = P(drawing Blue and red ball in any order)


P(Sany) = P(drawing Blue ball followed by red) + P(drawing Red ball followed by Blue)


Since drawing a ball is an independent event, the probabilities multiply each other.





.


The required probabilities are .


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