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A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:
(i) white (ii) red (iii) black (iv) not red
Medium
Solution
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Total no. of balls in the bag is 12 (3 red, 5 black and 4 white)
Solution(i):
No. of white balls in bag is 4
Therefore,
4
C
1
( Selecting 1 out of 4 items) times out of
12
C
1
( Selecting 1 out of 11 items) a white ball is picked.
Let E be the event of drawing a white ball from bag
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
12
C
1
4
C
1
=
12
4
=
3
1
Solution(ii):
No. of red balls in bag is 3
Therefore,
3
C
1
( Selecting 1 out of 3 items) times out of
12
C
1
( Selecting 1 out of 12 items) a red ball is picked.
Let E be the event of drawing a red ball from bag
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
12
C
1
3
C
1
=
12
3
=
4
1
Solution(iii):
No. of black balls in bag is 5
Therefore,
5
C
1
( Selecting 1 out of 5 items) times out of
12
C
1
( Selecting 1 out of 12 items) a black ball is picked.
Let E be the event of drawing a black ball from bag
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
12
C
1
5
C
1
=
12
5
Solution(iv):
No. of balls that are not red in bag is 9 (5 black, 4 white)
Therefore,
9
C
1
( Selecting 1 out of 9 items) times out of
12
C
1
( Selecting 1 out of 12 items) a ball that is not red is picked.
Let E be the event of drawing a ball that is not red from bag
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
12
C
1
9
C
1
=
12
9
=
4
3