Question

l) lf 25% of U.S. federal prison inmates are not US. citizens, find the probability that 2 randomly selected federal prison inmates will not be U.S. citizens. 2) Three cards are drawn from a deck without replacement. Find these probabilities. a. Al are jacks. b. All are clubs. c. All are red cards. For a recent year, 0.99 of the incarcerated population is adults and 0.07 is female. If an incarcerated person is selected at random, find the probability that the person is a female 3) given that the person is an adult. 4) U.S. growers harvested 11 billion bushels of com in 2005. About 1.9 billion bushels were exported, and 1.6 billion bushels were used for ethanol. Choose one bushel of corm at random. What is the probability that it was used either for export or for ethanol? 5) There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be selected if there must be 2 men and 2 women on the committee? How many ways can this committee be selected if there must be at least 2 women on the committee? 6) An advertising manager decides to have an ad campaign in which 8 special calculators will be hidden at various locations in a shopping mall. If he has 17 locations from which to pick, how many different possible combinations can he choose? 7) How many ways can an adviser choose 4 students from a class of 12 if they are all assigned the same task? How many ways can the students be chosen if they are each given a different task? 8) The probabilities that a customer will rent 0, 1, 2, 3, or 4 DVDs on a single visit to the rental store are 0.15, 0.25, 0.3, 0.25, and 0.05, respectively. A) Find the Mean B) Find the Variance C) Find the Standard Deviation. 9) A 45-year-old man purchases a $350,000 term life insurance policy for an annual payment of S450. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999. Find the expected value of the policy for the insurance company. 10) The probability that Jack parks in a no-parking zone and gets a parking ticket is 0.08, and the probability that Jack cannot find a legal parking space and has to park in the no- parking zone is 0.40. On Tuesday, Jack arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.

Answer 1

1.)

Probability of inmate not being a us citizen = 0.25

p(Two inmate are not citizen)=0.25*0.25=0.0625

2.)

There are total 52 cards in the deck

3 are drawing without replacement

a.)All are jack,: there are total 4 jack in the deck

P(All are jack)=

$=\frac{\binom{4}{1}}{52}*\frac{\binom{3}{1}}{51}*\frac{\binom{2}{1}}{50}$

$=\frac{4}{52}*\frac{3}{51}*\frac{2}{50}$

$=\frac{1}{5525}$

b.)all are club

There are 13 club in the deck

$P(All-Club)=\frac{\binom{13}{1}}{52}*\frac{\binom{12}{1}}{51}*\frac{\binom{11}{1}}{51}$

$=\frac{13}{52}*\frac{12}{51}*\frac{11}{50}$

$=\frac{11}{850}$

c.)

All red red cards

There are 26 red cards

$P(All-Red)=\frac{26}{52}*\frac{25}{51}*\frac{24}{50}$

$=\frac{2}{17}$