Theory question 115
Probability(a) Two items are selected at random from four items labeled (p, q, r, s) (i) list the sample space if sampling is done (α) with replacement; (β) without replacement. (ii) Find the probability that r is at least one of the two objects selected: (α) in a(i)
(b) How many whole numbers from 100 to 999 are divisible by: (i) 4; (ii) both 3 and 4
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(a)(i)(α) With replacement, 16 ordered pairs: pp, pq, pr, ps, qp, qq, qr, qs, rp, rq, rr, rs, sp, sq, sr, ss
(β) Without replacement, 12 ordered pairs: pq, pr, ps, qp, qr, qs, rp, rq, rs, sp, sq, sr
(ii) With replacement: pairs containing r are pr, qr, rp, rq, rr, rs, sr = 7, probability 7/16
Without replacement: pr, qr, rp, rq, rs, sr = 6 of 12, probability ½
(b)(i) 100, 104, ..., 996: 100 + 4(n − 1) = 996, n = 225
(ii) Divisible by both 3 and 4 means divisible by 12: 108, 120, ..., 996; 108 + 12(n − 1) = 996, n = 75
Divisible by both 3 and 4 is the same as divisible by 12.