Question

5. The probability that Abiola will be late to office on a given day is 2/5. In a given working week of six days, find, correct to four significant figures, the probability that he will:
(a) be late for only 3 days;
(b) not be late in the week;
(c) be late throughout the six days.

Accepted Answer

This is a binomial distribution with n=6, p(late)=2/5=0.4, q(not late)=3/5=0.6.
(a) P(exactly 3 late) = ⁶C₃(0.4)³(0.6)³ = 20×0.064×0.216 = 0.2765 (4 s.f.)
(b) P(not late all week) = (0.6)⁶ = 0.04666 (4 s.f.)
(c) P(late throughout) = (0.4)⁶ = 0.004096 (4 s.f.)

WAEC Further Mathematics 2022 Theory — Question 5

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