Theory question 115
Probability(a) The probability that a man wins a race is 0.8. In four different races, what is the probability that he wins: (i) all races; (ii) no race; (iii) at most 3 races?
(b) A class consists of 5 girls and 10 boys. If a committee of 5 is chosen at random from the class find the probability that: (i) 3 boys are selected; (ii) at least one girl is selected.
Show the model answer
Model answer
(a) p = 0.8, q = 0.2, n = 4.
(i) 0.8⁴ = 0.4096. (ii) 0.2⁴ = 0.0016. (iii) 1 − 0.4096 = 0.5904.
(b) ¹⁵C₅ = 3003.
(i) ¹⁰C₃ × ⁵C₂ = 120 × 10 = 1200; P = 1200/3003 = 400/1001 ≈ 0.400.
(ii) No girl: ¹⁰C₅ = 252; P(at least one girl) = 1 − 252/3003 = 131/143 ≈ 0.916.
Explanation
'At least one' is 1 minus 'none'.