Theory question 112
Probability(a) The probability that an athlete will not win any of the three races is ¼. If the athlete runs in all the races, what is the probability that the athlete will win: (i) only the second race; (ii) all the three races; (iii) only two of the races?
(b) A cone with perpendicular height 24cm has a volume of 24cm3. Find the volume of a cone with same base radius and height 84cm. [Take π = 22/7]
Show the model answer
Model answer
(a) Taking P(lose a race) = ¼ and P(win a race) = ¾ for each race:
(i) P(L W L) = ¼ × ¾ × ¼ = 3/64
(ii) P(W W W) = (¾)3 = 27/64
(iii) P(LWW) + P(WLW) + P(WWL) = 3 × (¾ × ¾ × ¼) = 27/64
(b) Same base radius, so volume is proportional to height
V = 24 × 84/24 = 84 cm3
Explanation
For (b), keep r fixed: V = ⅓πr2h grows in step with h.