Theory question 106
Sets(a) M = {n: 2n − 3 ≤ 37}, where n is a counting number.
(i) Write down all the elements in M.
(ii) If a number is selected at random from M, what is the probability that it is a: (α) multiple of 3; (β) factor of 10.
(b) A shopowner gave an end-of-year bonus to two of his attendants, Kontor and Gapson in the ratio of their ages. Kontor's age is one and half times that of Kontor who is 20 years old. If Kontor received Le 200,000.00: find: (i) the total amount shared; (ii) Gapson's share.
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(a)(i) 2n ≤ 40 ⇒ n ≤ 20, so M = {1, 2, 3, …, 20}
(ii)(α) Multiples of 3: 3, 6, 9, 12, 15, 18 ⇒ P = 6/20 = 3/10
(β) Factors of 10: 1, 2, 5, 10 ⇒ P = 4/20 = 1/5
(b) Gapson is 20, so Kontor is 1½ × 20 = 30; ratio Kontor : Gapson = 3 : 2
(i) 3/5 of total = Le 200,000 ⇒ total = Le 333,333.33 (= 1,000,000/3)
(ii) Gapson's share = 2/5 of total = Le 133,333.33 (= 400,000/3)
Read (b) as 'one and half times that of Gapson, who is 20 years old'.