Q. 94.3( 3 Votes )

A bag contains 5 white, 7 red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

Answer :

There are 5 white, 7 red and 3 black balls in the bag, so the number of all favorable outcomes in the sample space is


n(S) = 5+7+3=15


Let A be the event of getting a red ball in the first draw. Hence the probability becomes


(as there are 7 red balls out of 15 balls)


Let B represents the event of getting a red ball in the second draw. Hence the probability becomes


(as there are 7 red balls and one red ball is already drawn in first draw so now there are total of 6 red balls)


Let C represents the event of getting a red ball in the third draw. Hence the probability becomes


(as there are 7 red balls and two red balls are already drawn in first and second draw so now there are total of 5 red balls)


Then the probability of none being red balls without replacement







Hence the required probability is


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