Theory question 113
ProbabilityA survey conducted revealed that four out of every twenty taxi drivers do not have valid driving license. If 6 drivers are selected at random, calculate, correct to three decimal places, the probability that: (a) exactly 2; (b) more than 3; (c) at least 5 have valid driving license.
Show the model answer
Model answer
P(valid) = 16/20 = 0.8, P(not valid) = 0.2; binomial with n = 6
(a) 6C2(0.8)2(0.2)4 = 15 × 0.64 × 0.0016 = 0.015
(b) P(4) + P(5) + P(6) = 0.24576 + 0.393216 + 0.262144 = 0.901
(c) P(5) + P(6) = 0.393216 + 0.262144 = 0.655
Explanation
Four out of twenty have no licence, so the probability of a valid licence is 0.8.