Theory question 110
Probability(a) The probabilities that three boys pass an examination are 2/3, 5/8 and 3/4 respectively. Find the probability that: (i) all the boys pass; (ii) none of the boys pass; (iii) only two of the boys pass.
(b) A shopkeeper marks a television set for sale at N36,000 so as to make a profit of 20% on the cost price. When he sells it, he allows a discount of 5% off the marked price. Calculate the actual percentage profit.
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(a)(i) 2/3 × 5/8 × 3/4 = 30/96 = 5/16.
(ii) 1/3 × 3/8 × 1/4 = 3/96 = 1/32.
(iii) Exactly two pass: 2/3 × 5/8 × 1/4 + 2/3 × 3/8 × 3/4 + 1/3 × 5/8 × 3/4 = 10/96 + 18/96 + 15/96 = 43/96.
(b) Cost price = 36,000 ÷ 1.2 = N30,000. Selling price = 95% of 36,000 = N34,200.
Profit = N4,200; actual percentage profit = 4,200/30,000 × 100% = 14%.
For 'only two pass' add the three cases where exactly one boy fails.