Theory question 115
Probability(a) Two pupils are chosen at random from a group of 4 boys and 5 girls. Find the probability that the two pupils chosen would be boys.
(b) Twenty percent of the total production of transistors produced by a machine are below standard. If a random sample of 6 transistors produced by the machine is taken, what is the probability of getting; (i) exactly 2; (ii) exactly 1; (iii) at least 2; (iv) at most 2, standard transistor(s)?
Show the model answer
(a) ⁴C₂/⁹C₂ = 6/36 = 1/6
(b) Let X = number of standard transistors; p(standard) = 0.8, q = 0.2, n = 6
(i) P(X = 2) = ⁶C₂(0.8)²(0.2)⁴ = 15 × 0.64 × 0.0016 = 0.01536
(ii) P(X = 1) = 6(0.8)(0.2)⁵ = 0.001536
(iii) P(X ≥ 2) = 1 − P(0) − P(1) = 1 − 0.000064 − 0.001536 = 0.9984
(iv) P(X ≤ 2) = 0.000064 + 0.001536 + 0.01536 = 0.01696
Use the binomial distribution with p = 0.8 for a standard transistor.