Me and my group have been struggling to figure out this prob

Me and my group have been struggling to figure out this probability problem. So please show us a step by step solution to it and if possible, explain the logic as it is equally as important as the answer.

Solution

a) Prob that all 3 workers selected from each city are super commuters

= product of 3 probabilities (as events are independent)

= 0.13(0.086)(0.075)

= 0.08385

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b) Prob that none are super commuters =

Product of non super commuters for 3 cities

= 0.87(0.914)(0.925)

=0.7355415

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c) Prob for only one from Houston super commuter

= 0.13(0.914)(0.925)

= 0.1099085

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d) Prob that exactly 2 are super commuters

= Prob any two cities super commuters and third city non super commuter

= 0.13(0.086)(0.925)+(0.13)(0.914)(0.075)+(0.87)(0.086)(0.075)

= 0.01034+0.00891+0.05611

= 0.07536