A manufacturer produces three different models of computer: 50% are Ace, 30% are

Question

A manufacturer produces three different models of computer: 50% are Ace, 30% are wer and 20% are Intromodel. They have failure prababilities of 1%, 5% and 8% Maxpo respectively (a) Find the probability i) that a machine is a Maxpower. given that it has failed; [3 marksl iii) that if 3 machines are chosen at random, they are all the same model. [3 marks] (b) Use a suitable approximation to find that probability that, in a random selection of 40 machines, there are more than 15 and less than 25 Aces. [6 marks]

Explanation / Answer

(2)

From given data,

(i) The probability of a computer chosen fails,

P(Ace & Fails) = 0.5 * 0.01 = 0.005

P(MaxP & Fails) = 0.3 * 0.05 = 0.015

P(Int & Fails) = 0.2 * 0.08 = 0.016

Hence required probability = 0.005 + 0.015 + 0.016 = 0.036

(ii) Probability of machine is a maxpower given that it has failed i.e. P(MaxP|Failed)

P(MaxP|Failed) = {P(Ace&Fails)} / {P(Ace & Fails)+P(MaxP&Fails)+P(Int&Fails)}

P(MaxP|Failed) = 0.015 / 0.036 = 0.4167

(iii) If three machines are chosen, they are of same model

P(A) = All three machines are chosen of type Ace = (0.5)^3

P(B) = All three machines are chosen of type MaxPower = (0.3)^3

P(C) = All three machines are chosen of type IntroModel = (0.2)^3

Hence, required probability = P(A) + P(B) + P(C) = 0.125 + 0.027 + 0.008 = 0.16

P(Ace) 0.5 P(MaxP) 0.3 P(Int) 0.2

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