2.The probability that carAwill rise in price is0.5while the probability that carBwill rise in price is0.57. The probability of both cars rising in price is0.41.

A= carAwill rise in price B= carBwill rise in price Report numeric answers to 2 decimal places.Do notconvert to percent. 1. Use the given information to complete the following probability table. AandBrepresent the complements of eventsAandBrespectively.

B B Total

A A Total 1.00

2. What is the probability that a) carAwill not rise in price? b) only carBwill rise in price? c) at least one car will rise in price? d) both cars will not rise in price? e) only one car will rise in price (not both)? f) no more than one car will rise in price? 3. a) AreAandBmutually exclusive? Why? Select an answerNo. Occurrence of one affects the probability of the other.No. P(A and B) = 0Yes. Occurrence of one affects the probability of the other.Yes. Occurrence of one does not affect the probability of the other.Yes. They cannot occur at the same time.No. P(A and B) P(A)P(B)No. Occurrence of one does not affect probability of the other.Yes. P(A and B) 0Yes. They can occur at the same time.No. P(A and B) 0No. They cannot occur at the same.

b) AreAandBindependent? Why?Select an answerNo. Occurrence of one does not affect probability of the other.Yes. Occurrence of one does not affect the probability of the other.Yes. Occurrence of one affects the probability of the other.No. P(A and B) = 0No. P(A and B) P(A)P(B)Yes. P(A and B) 0No. They cannot occur at the same.No. They can occur at the same.Yes. P(A and B) P(A)P(B)Yes. They cannot occur at the same time.Yes. They can occur at the same time.No. P(A and B) = P(A)P(B).

3.Suppose61%of batteries obtained from a major supplier last beyond warranty period. A random sample of23batteries is selected. Assuming independence, use the binomial formula or software (recommended) to answer the following questions.

1. What is the probability that, of the23batteries selected: (Report probabilities accurate toat least 4decimal places.)

a)exactly 14last beyond warranty period? b)exactly 10do notlast beyond warranty period? c)allof them last beyond warranty period? d)at most 13last beyond warranty period? e)at least 12last beyond warranty period? f)more than halflast beyond warranty period? g)at least 12butno more than 16last beyond warranty period? h)less than 11ormore than 14last beyond warranty period?

2. Calculate the mean and standard deviation of batteries that last beyond warranty period. Round to 2 decimal places.

Mean = Standard Deviation =

3. If you expect to find exactly84batteries that last beyond warranty period, how large a sample should you select? Report the minimum sample size required as an integer.

4. SupposeXhas a binomial distribution withn=12=12andp=0.17=0.17.X=0,1,2,...,12=0,1,2,...,12. Determine the following probabilities. Use software. Rounding is not necessary. If you must round, keep at least 4 decimal places. 1. P(X=3)=(=3)=

2. P(X1)=(1)=

3. P(X3)=(3)=

4. P(X<15)=(<15)=

5. P(X3)=(3)=

6. P(X=1.9)=(=1.9)=

7. P(X>1.9)=(>1.9)=

8. P(1X4)=(14)=

9. P(1

10. P(0