A shop in second-hand electronic equipment sells three types of microphones. Typ

Question

A shop in second-hand electronic equipment sells three types of microphones. Type i microphones are working properly with probability p_i where p_1 = 0.8, p_2 = 0.9 and p_3 = 1. Arjan buys a microphone at random, meaning that with probability 1/3 he buys a type i microphone, i = 1, 2, 3. Define and use notation for relevant event(s) and/or random variable(s) to find the following. a. The probability that the purchased microphone is working properly. b. The probability that the purchased microphone is of type 3 when it turns out to be working properly.

Explanation / Answer

a) P(Working Properly) = 1/3*0.8+1/3*0.9+1/3*1 = 0.9

b) P(Type3/Working properly) = (1*1/3)/0.9 = 0.370 (rounded to three decimal places)

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