Step by step of how to do numbers 15, 16, 17 and what formula was used from the

Question

Step by step of how to do numbers 15, 16, 17

and what formula was used from the formula sheet

please use as much detail as possible

And if possible explain when you would use each formula on the refernce sheet

Thank you!

15. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000 if the residents of a household own 2 cars is about: a) b) c) 42% 49% 62% 69% Base Construction Inc. and Olive Construction Inc. are local competitors who bid on some public construction projects from time to time. Base Inc. bids on 70% of projects. When Olive Inc. knows that Base Inc. does not bid on a given project, they bid on that project 50% of the time. However, when Olive Inc. knows that Base Inc. bids on a given project, they bid on that project only 25% of the time. 16. Compute the probability of an event that Base Construction Inc. does not bid on a randomly selected project and Olive Construction Inc. bids on that random project. a) 17.5% ) 15% c) 12.5% d) 10% 17. Compute the probability of an event that Base Construction Inc. does not bid on a randomly selected project, knowing that Olive Construction Inc. bids on that random project. a) b) c) 40% 42% 44% 46%

Explanation / Answer

Question 15:

Here, we are given that:

P( own 2 cars | > 50,000 ) = 0.8

P( > 50,000) = 0.6
P( own 2 cars ) = 0.7

Using Bayes theorem, we get here:

P( own 2 cars and >50,000) = P( own 2 cars | > 50,000 )P(> 50,000) = 0.8*0.6 = 0.48

Now using bayes theorem again, we get here:

P( > 50,000 | own 2 cars ) = P( own 2 cars and >50,000) / P( own 2 cars ) = 0.48 / 0.7 = 0.69

Therefore d) 0.69 is the required probability here.

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