Theory question 113
ProbabilityA survey indicated that 65% of the families in an area have cars. Find, correct to three decimal places, the probability that among 7 families selected at random in the area (a) exactly 5; (b) 3 or 4; (c) at most 2 of them have cars.
Show the model answer
Model answer
Binomial with n = 7, p = 0.65, q = 0.35
(a) 7C5(0.65)5(0.35)2 = 0.298
(b) P(3) + P(4) = 0.1442 + 0.2679 = 0.412
(c) P(0) + P(1) + P(2) = 0.0006 + 0.0084 + 0.0466 = 0.056
Explanation
Use P(r) = ⁿCᵣ pʳ qⁿ⁻ʳ and add the cases needed.