Nov 2002 P1 Q16
(1) Two unbiased dice are thrown.
Find the probability that they
(i) show the same number
(ii) show different number
(2) Three unbiased dice are thrown.
Find the probability that
(i) they all show different numbers
(ii) at least two show the same number
Answer:
(1)
(i) P(both shows same number) = 1/6 * 1/6 * 6 (6 different numbers) = 1/6
(ii) P(both shows different number) = 1 - both show same number = 5/6
(2)
(i) P(all different numbers) = P(first 2 dice are different and 3rd dice is also different number)
= P(first 2 dice different) * P(3rd dice different number from first 2 dice)
= 5/6 * 4/6 (4 numbers out of 6 left since the first 2 dice have already taken/used up 2 numbers)
= 5/9
(ii) P (at least two show same number) = 1 - P(all different numbers) = 4/9
