b) A bag contains 5 black and 7 white balls. A second bag contains 8 black and 3 white balls. One bag is selected at random and a ball is drawn
from it. Find the probability that the ball drawn is white. (15 marks)
Answers
Answer:
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,
7
C
1
( Selecting 1 out of 7 items) times out of
15
C
1
( 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) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
15
C
1
7
C
1
=
15
7
Solution(ii):
No. of black or white balls in bag is 8 (5 black and 3 white)
Therefore,
8
C
1
( Selecting 1 out of 8 items) times out of
15
C
1
( 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) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
15
C
1
8
C
1
=
15
8
Solution(iii):
No. of non-black balls in bag is 10 (7 red and 3 white)
Therefore,
10
C
1
( Selecting 1 out of 10 items) times out of
15
C
1
( 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) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
15
C
1
10
C
1
=
15
10
=
3
2
Step-by-step explanation:
TOTAL NO OF BALLS IN BOTH BAGS = 5+7+8+3=23
TOTAL NO OF WHITE BALLS IN BOTH BAGS = 7+3=10
TOTAL NO OF BLACK BALLS IN BOTH BAGS= 8+5=13
P(WHITE BALLS) =NO OF WHITE BALLS / TOTAL NO OF BALLS
= 10/23