Theory question 114
Probability(a) Eight coins are tossed once. Find, correct to three decimal places, the probability of obtaining (i) exactly 8 heads; (ii) at least 5 heads; (iii) at most 1 head.
(b) In how many ways can four letters from the word SHEEP be arranged (i) without any restriction; (ii) with only one E.
Show the model answer
Model answer
(a) Binomial with n = 8, p = ½; each outcome count over 256
(i) 1/256 ≈ 0.004
(ii) (56 + 28 + 8 + 1)/256 = 93/256 ≈ 0.363
(iii) (1 + 8)/256 = 9/256 ≈ 0.035
(b)(i) Four different letters S, H, E, P: 4! = 24; two E's with two of S, H, P: 3 × 4!/2! = 36; total 60
(ii) One E with S, H, P: 4! = 24
Explanation
Count arrangements with repeated letters by dividing by the factorial of the repeats.