Can anyone help with this? I need to show all of the steps. 3. Tom is a lead eng

Question

Can anyone help with this? I need to show all of the steps.

3. 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 will 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) (Continuing from part (b)) Given that the phone was still working after a week, what is the probability that the design was flawed?

Explanation / Answer

a) 2 engg can be drawn from 8 engg in 8C2 ways
For each of the above cases 2 engg can be drawn from remaining 6 engg in 6C2 ways
For each of the above cases 2 engg can be drawn from remaining 4 engg in 4C2 ways
So possible combination of making 4 groups of 2 engg = 8C2 * 6C2 * 4C2 = 2520 ways.

b) Probability of being flawed = 0.2 ; P(not being flawed) = 0.8
If flawed, probability of being working after 1 week = 1-0.8 = 0.2
If not flawed, probability of being working after 1 week = 0.9
P(working after 1 week)= (0.2*0.2) + (0.8 * 0.9) = 0.76

c) P(design is flawed | working after 1 week) = P(design is flawed working after 1 week)/ P(working after 1 week) = (0.2 * 0.2)/ 0.76 = 0.0526

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