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Question

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:
(i) red (ii) black or white (iii) not black

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Solution

Total no. of balls in the bag is 15 (7 red, 5 black and 3 white)

Solution(i):
No. of red balls in bag is 7
Therefore, 7C1( Selecting 1 out of 7 items) times out of 15C1( Selecting 1 out of 15 items) a red ball is picked.

Let E be the event of drawing a red ball from bag

We know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=7C115C1=715

Solution(ii):
No. of black or white balls in bag is 8 (5 black and 3 white)
Therefore, 8C1( Selecting 1 out of 8 items) times out of 15C1( Selecting 1 out of 15 items) a black or white ball is picked.

Let E be the event of drawing a black or white ball from bag

We know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=8C115C1=815

Solution(iii):
No. of non-black balls in bag is 10 (7 red and 3 white)
Therefore, 10C1( Selecting 1 out of 10 items) times out of 15C1( Selecting 1 out of 15 items) a non-black ball is picked.

Let E be the event of drawing a non-black ball from bag

We know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=10C115C1=1015=23


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