HW #6 – Probability(Solutions)



HW #19 – Probability(Solutions)

2. A) 25% B) 20%

3. In the diagram, first 1% was filled in. Then since the “INF” circle has to add up to 3%, I filled in the 2% section. Then since the “FAIL” circle has to add up to 14% I filled in the 13% section. Finally the outside 84% was obtained since all four numbers have to add up to 100%. Note that the surgeries that are free from infection and successful are the 84%.

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7. .6396

8. It is much easier to find the opposite and subtract from 1. The opposite of at least one person having such a birthday is nobody having such a birthday. Below is the only branch of the tree diagram in which this happens. Once the probability of this path is found we subtract from 1.

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Answer is [pic]

12. C) .8667 D) .9286

13. B) P(no inf | successful) = P(no inf & successful) / P(successful) = .84/.86 = .9767

C) P(successful | no inf) = P(successful & no inf) / P(no inf) = .84/.97 = .8660

Note that I first used the formula P(A|B)=P(A&B)/P(B) and the both P(A&B) and P(B) are found in the Venn Diagram above.

16.

B) 37.07%

C) 1183/4327 = 27.34%

G) .5224

H) P(female assistant) = P(female & assistant) / P(assistant) = (565/4327)/(1183/4327) = 565/1183 = .4776 Note that I first used the formula P(A|B)=P(A&B)/P(B) and the both P(A&B) and P(B) are found in the table in the problem.

L) .2270

M) P(assistant | female) = P(assistant & female) / P(female) = (565/4327)/(1604/4327) = 565/1604 = .3522 Note that I first used the formula P(A|B)=P(A&B)/P(B) and the both P(A&B) and P(B) are found in the table in the problem.

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