Theory question 113
Probability(a) A fair die with six faces is thrown six times. Calculate, correct to three decimal places, the probability of obtaining (i) exactly three sixes; (ii) at most three sixes.
(b) Eight percent of screw produced by a machine are defective. From a random sample of 10 screws produced by the machine, find the probability that: (i) exactly two will be defective; (ii) not more than two will be defective.
Show the model answer
Model answer
(a) Binomial n = 6, p = 1/6
(i) 6C3(1/6)3(5/6)3 = 2500/46656 ≈ 0.054
(ii) 1 − [P(4) + P(5) + P(6)] = 1 − (375 + 30 + 1)/46656 = 46250/46656 ≈ 0.991
(b) Binomial n = 10, p = 0.08
(i) 10C2(0.08)2(0.92)8 ≈ 0.148
(ii) P(0) + P(1) + P(2) = 0.4344 + 0.3777 + 0.1478 ≈ 0.960
Explanation
For 'at most three' it is quicker to subtract P(4), P(5) and P(6) from 1.