As a rule of thumb, round your answers to 4 decimal places as needed 3 1 Suppose P (A) 0 2, P (B A) 0 4, P (B Ac) 0 5 3 1 a Find P(B) Hint Law of total probability 3 1 b Find P(A B) Hint Bayes Theorem 3 2 Mina has applied for a job with Facebook As part of the hiring process, Facebook will of course look at her grade in BUS 190 at SJSU If Mina gets an A, theres a 65 chance that Facebook will hire her But if she does not get an A, theres only a 10 chance that they will hire her Theres an 80 chance that Mina will get an A in BUS 190 3 2 a What is the probability that Facebook will hire Mina 3 2 b It turns out that Facebook does hire Mina What is the probability that she got an A in BUS 190 3 3 In a study of pleas and prison sentences, it is found that 40 of the subjects studied were sent to prison Among those sent to prison, 20 chose to plead guilty Among those not sent to prison, 10 chose to plead guilty 3 3 a If a study subject is randomly selected, what is the probability that this person was not sent to prison 3 3 b Ifastudysubjectisrandomlyselected,whatistheprobabilitythatthisstudysubjectenteredaguiltyplea 3 3 c Ifastudysubjectisrandomlyselectedanditisthenfoundthatthissubjectenteredaguiltyplea,findtheprobabilitythatthispersonwasnotsenttoprison 3 4 An oil company purchased an option on land in Alaska Preliminary geologic studies assigned the following prior probabilities P (find high quality oil) 0 50 P (find medium quality oil) 0 20 P (find no oil) 0 30 After 200 feet of drilling on the first well, a soil test is made The probabilities of finding a special type of soil (i e soil XYZ) identified by the tests are P (find soil XYZ find high quality oil) 0 30 P (find soil XYZ find medium quality oil) 0 50 P(find soil XYZ find no oil) 0 20 3 4 a (0 5 pt) What is the probability of finding oil 3 4 b (0 5 pt) What is the probability of finding soil XYZ 3 4 c (0 5 pt) What is the probability of finding oil given that soil XYZ is found in the test Hint P (Find oil Find soil XYZ) 1 P (Find no oil Find soil XYZ)

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As a rule of thumb, round your answers to 4 decimal places as needed. 3.1. Suppose P (A) = 0.2, P (B|A) = 0.4, P

As a rule of thumb, round your answers to 4 decimal places as needed.

3.1. Suppose P (A) = 0.2, P (B|A) = 0.4, P (B|Ac) = 0.5. 3.1.a Find P(B). [Hint: Law of total probability.]

3.1.b Find P(A|B). [Hint: Bayes Theorem.]

3.2. Mina has applied for a job with Facebook. As part of the hiring process, Facebook will of course look at her grade in BUS 190 at SJSU. If Mina gets an A, theres a 65% chance that Facebook will hire her. But if she does not get an A, theres only a 10% chance that they will hire her. Theres an 80% chance that Mina will get an A in BUS 190.

3.2.a What is the probability that Facebook will hire Mina?
3.2.b It turns out that Facebook does hire Mina. What is the probability that she got an A in BUS 190?

3.3. In a study of pleas and prison sentences, it is found that 40% of the subjects studied were sent to prison. Among those sent to prison, 20% chose to plead guilty. Among those not sent to prison, 10% chose to plead guilty.

3.3.a If a study subject is randomly selected, what is the probability that this person was not sent to prison?
3.3.b Ifastudysubjectisrandomlyselected,whatistheprobabilitythatthisstudysubjectenteredaguiltyplea?
3.3.c Ifastudysubjectisrandomlyselectedanditisthenfoundthatthissubjectenteredaguiltyplea,findtheprobabilitythatthispersonwasnotsenttoprison.

3.4. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

P (find high quality oil) = 0.50 P (find medium quality oil) = 0.20

P (find no oil) = 0.30

After 200 feet of drilling on the first well, a soil test is made. The probabilities offinding a special type of soil (i.e. soil XYZ) identified by the tests are:

P (find soil XYZ | find high quality oil) = 0.30 P (find soil XYZ | find medium quality oil) = 0.50 P(find soil XYZ | find no oil) = 0.20

3.4.a (0.5 pt) What is the probability of finding oil?

3.4.b (0.5 pt) What is the probability of finding soil XYZ?

3.4.c (0.5 pt) What is the probability of finding oil given that soil XYZ is found in the test? [Hint: P (Find oil | Find soil XYZ) = 1 P (Find no oil | Find soil XYZ).]