Tom is a lead engineer in charge of a team of 8 electrical engineers. His job is

Question

Tom is a lead engineer in charge of a team of 8 electrical engineers. His job is to design a cellu lar phone (handset). The handset consists of 4 components - antenna, circuitry, LCD screen, and software. (a) In how many different ways can Tom form 4 groups of 2 engineers in each for designing the 4 components? (b) The overall design of the handset put together by Tom's team will be flawed with probability 0.2. If the design is flawed, the phone wll not be working after a week with probability 0.8. If the design is not flawed, it will continue to work after a week with probability 0.9. Compute the probability that the phone will be working after a week. (c) (Continuin g from part (b) Given that the phone was stll working after a week, what is the probability that the design was flawed?

Explanation / Answer

(a) First the no of ways in which 2 can e selected fro 8 peoples;
= 8C2 * 6C2 * 4C2* 2C2
=(8!/6!*2!)*(6!/4!*2!)*(4!/2!*2!)*(2!/2!*0!)
=2520

Second the no of ways in which 2 can be arranged among 4 groups ; since the arrangement will vary hence simple factorial of will be the choice which is 4!

So finally you need to divide the former by later to get the answer
=2520/4!
=105 ANSWER

(b) if the device is flawed the phone will working after week probability = 0.2 (1 - 0.8) = 0.04

if the device is not flawed the phone will working after week probability = (1-0.2) 0.9 = 0.72

so the  phone will working after week probability = 0.04 + 0.72 = 0.76

(c) P = 0.04(flawed phone) / 0.76(total phone working after one week ) = 0.052

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