Theory question 112
Probability(a) An association is made up of 6 farmers and 8 traders. If an executive body of 4 members is to be formed, find the probability that it will consist of at least two farmers.
(b) The probability of an accident occuring in a given month in factories X, Y, and Z are 1/5, 1/12 and 1/6 respectively. Find the probablity that the accident will occur in: (i) none of the factories; (ii) all the factories; (iii) at least one factory.
Show the model answer
Model answer
(a) ¹⁴C₄ = 1001. 2 farmers: 15 × 28 = 420; 3: 20 × 8 = 160; 4: 15. P = 595/1001 = 85/143 ≈ 0.594.
(b)(i) (4/5)(11/12)(5/6) = 11/18.
(ii) (1/5)(1/12)(1/6) = 1/360.
(iii) 1 − 11/18 = 7/18.
Explanation
'At least one' = 1 − P(none).