Q. 154.0( 4 Votes )

A bag contains 7 white, 5 black and 4 red balls. Four balls are drawn without replacement. Find the probability that at least three balls are black.

Answer :

Given:


Bag contains 7 white, 5 black and 4 red balls


It is told that four balls are drawn without replacement.


We need to find the probability that at least three balls drawn are Black.


The possible cases of drawing balls are as shown below:


i. Black, Black, Black, Others


ii. Black, Black, Others, Black


iii. Black, Others, Black, Black


iv. Others, Black, Black, Black


v. Black, Black, Black, Black


P(Dat3blacks) = P(BBBO) + P(BBOB) + P(BOBB) + P(OBBB) + P(BBBB)


Since drawing balls are independent events so, the probabilities multiply each other.







The required probability is .


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