Question

12(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 1200cm³. Find the value of a cone with same base radius and height 84cm. [Take π=22/7].

Accepted Answer

(a) P(athlete will not win)=¼, so P(athlete will win)=1−¼=¾.
(i) P(wins only the second race) = P(loses 1st)×P(wins 2nd)×P(loses 3rd) = ¼×¾×¼ = 3/64.
(ii) P(wins all three) = ¾×¾×¾ = 27/64.
(iii) P(wins exactly two) = P(W,W,L)+P(W,L,W)+P(L,W,W) = 3×(¾×¾×¼) = 27/64... per source's detailed calc, P(winning two) = 9/64+9/64+9/64 = 27/64 (0.42).

(b) First obtain the radius of the first cone using given volume: 1200 = (22/7)r²(24). r²=1200×7/(22×24)=8400/528=15.909, r=3.989cm.
For the second cone (same radius, height 84cm): V=(22/7)×15.909×84 = 4200cm³.

WAEC Mathematics 2022 Theory — Question 12

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