Theory question 104
ProbabilityA man has 9 identical balls in a bag. Out of these, 3 are black, 2 are blue and the remaining are red.
(a) If a ball is drawn at random, what is the probability that it is (i) not blue? (ii) not red?
(b) If 2 balls are drawn at random, one after the other, what is the probability that both of them will be (i) black, if there is no replacement? (ii) blue, if there is a replacement?
Show the model answer
Model answer
Red balls = 9 − 3 − 2 = 4
(a)(i) P(not blue) = 1 − 2/9 = 7/9 (ii) P(not red) = 1 − 4/9 = 5/9
(b)(i) 3/9 × 2/8 = 1/12
(ii) 2/9 × 2/9 = 4/81
Explanation
Without replacement, both the number of black balls and the total drop by one for the second draw.