Theory question 115
ProbabilityA bag contains 4 red, 6 blue and 8 green identical marbles.
(a) If three marbles are drawn at random, without replacement, calculate the probability that: (i) all will be green; (ii) all will have the same colour.
(b) If each marble is replaced before another is drawn, calculate the probability that all will have the same colour.
Show the model answer
Model answer
Total 18 marbles
(a)(i) (8/18)(7/17)(6/16) = 336/4896 = 7/102
(ii) P(GGG) + P(BBB) + P(RRR) = 7/102 + (6 × 5 × 4)/4896 + (4 × 3 × 2)/4896 = (336 + 120 + 24)/4896 = 480/4896 = 5/51
(b) (8/18)3 + (6/18)3 + (4/18)3 = (512 + 216 + 64)/5832 = 792/5832 = 11/81
Explanation
Without replacement the numbers on top and bottom both drop by one each draw.