Step-by-step explanation:
Total number of balls in the bag = 13.
3 balls can be drawn in C(13,3) ways.
(a) Given that there are 5 white balls, 3 balls are drawn.
= C(5,3) ways.
(b) Given that there are 8 red balls, 3 balls are drawn.
= C(8,3) ways.
(i) Balls are replaced:
Probability of drawing 3 white balls in the first trial:
= C(5,3)/C(13,3)
= 10/286
= 5/143
Probability of drawing 3 red balls in the second trial:
= C(8,3)/C(13,3)
= 56/286
= 28/143
∴ Required Probability = (5/143) * (28/143)
= 140/20449.
(ii) Balls are not replaced:
Probability of drawing 3 white balls in the first trial:
= C(5,3)/C(13,3)
= 10/286
= 5/143
When the 3 white balls are drawn without replacement, the bag contains only 2 white balls and 8 red balls.
In the second trial, 3 balls can be drawn from 10 balls(8 + 2) in C(10,3) ways and 3 red balls can be drawn from 8 balls in C(8,3) ways.
Probability of drawing 3 red balls in the second trial:
= C(8,3)/C(10,3)
= 56/120
= 7/15
∴ Required Probability = (5/143) * (7/15)
= 35/2145
= 7/429
Hope it helps!