8.)Determine whether the events E and F are independent or dependent. Justify yo

Question

8.)Determine whether the events E and F are independent or dependent. Justify your answer.

a.) E: The battery in your cell phone is dead.

F: The batteries in your calculator are dead.

b.) E: Your favorite color is blue.

F: Your friend’s favorite hobby is fishing.

a.) E: You are late for school.

F: Your car runs out of gas.

18.)Life Expectancy The probability that a randomly selected 40-year-old female will live to be 41 years old is 0.99855 according to the National Vital Statistics Report, Vol. 56, No. 9.

   a.) What is the probability that two randomly selected 40-year-old females will live to be 41 years old?

    b.)What is the probability that five randomly selected 40-year-old females will live to be 41 years old?

   c.) What is the probability that at least one of five randomly selected 40-year-old females will not live to be 41 years old? Would it be unusual if at least one of five randomly selected 40-year-old females did not live to be 41 years old?

6.) find the value of each factorial. a.) 7!

12.) find the value of each permutation.   a.) 7P2

20.) find the value of each combination. a.) 9C2

32.)Clothing Options A woman has five blouses and three skirts. Assuming that they all match, how many different outfits can she wear?

34.)Arranging Students In how many ways can 15 students be lined up?

46.)Betting on the Perfecta In how many ways can the top 2 horses finish in a 10-horse race?

52.)Simple Random Sample How many different simple random samples of size 7 can be obtained from a population whose size is 100?

56.)DNA SequencesHow many distinguishable DNA sequences can be formed using one A, four Cs, three Gs, and four Ts?

62.)

Selecting a Committee Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly.

   a.) What is the probability that the committee is composed of all Democrats?

   b.) What is the probability that the committee is composed of all Republicans?

c.) What is the probability that the committee is composed of three Democrats and four Republicans?

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Explanation / Answer

8. When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin.

a. Cell phone and calculator not related to each other hence they are independent.

b. Your favourite color and your friends hobby are not related so they are independent.

c. You can be late because your car runs out of gas so they are not independent.

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