Theory question 105
Probability(a) In a game, a fair die is rolled once and two unbiased coins are tossed once. What is the probability of obtaining 3 and a tail?
(b) A box contains 10 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting: (i) a red, then a black marble; (ii) two black marbles.
Show the model answer
Model answer
(a) P(3 on the die) = 1/6
Two coins: HH, HT, TH, TT; exactly one tail in 2 of the 4 outcomes, so P(a tail) = 1/2
P(3 and a tail) = 1/6 × 1/2 = 1/12
(If 'a tail' is read as at least one tail, P = 3/4 and the answer is 1/6 × 3/4 = 1/8.)
(b)(i) P(red then black) = 3/10 × 7/9 = 21/90 = 7/30
(ii) P(two black) = 7/10 × 6/9 = 42/90 = 7/15
Explanation
Without replacement, the second fraction uses one fewer marble in total.