Theory question 105
ProbabilityA box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that: (a) three are red; (b) the first is blue and the other two are red; (c) two are white and one is blue.
Show the model answer
Model answer
Total = 36 balls
(a) P(3 red) = 12/36 × 11/35 × 10/34 = 11/357
(b) P(blue, red, red) = 8/36 × 12/35 × 11/34 = 44/1785
(c) One order (W, W, B): 16/36 × 15/35 × 8/34 = 32/714 = 16/357
The blue ball can be 1st, 2nd or 3rd, so P = 3 × 16/357 = 16/119
(If the order white, white, blue is intended, the answer is 16/357.)
Explanation
Without replacement, each draw has one ball fewer in the box.