2 . A card is randomly selected from a standard 52-card deck of playing cards.Determine the probability that the randomly selected card:

Enter probability as a fraction or as a decimal rounded to nearest thousandth (three places).Examples of correctly entered responses:

3/55/110.3000.6500.971

a.is red

b.is a "face card" (king, queen, or jack):

c.is the "jack of clubs"

d.is a heart and a diamond:

3. A family includes three children.Determine the probability that:

a.there are two boys and one girl

b. there isat leastone boy

c. there are children of both sexes

d. there isat mostone girl:

4. A jar contains four marbles labeled "1" , "2" , "3" , and "4".TWO marbles are drawn without replacement.Determine the probability

that:

a.the sum of the numbers on the drawn marbles = 5

b.the sum of the numbers on the drawn marbles is an odd number

c.the sum of the numbers on the drawn marbles = 9

d.one of the marbles drawn is the "3" marble

5. Determine whether the following pairs of events are mutually exclusive:

a.A= {A person earns more than $25,000}B= {A person earns less than $20,000}

Enter "yes" or "no" for answer

b. A card is drawn from a deck:C= {It is a King}D= {It is a heart}

c. A single, fair, 6-sided die is rolled:E= {An even number shows}F= {A number greater than 3 shows}

d. Three fair coins are tossed:G= {Two heads come up}H= {At least one tail comes up}

e. A family has three children:K= {First born is a boy}L= {The family has children of both sexes}

6. A single card is randomly drawn from one standard 52-card deck of playing cards, and eventsCandDare as follows:C= {the card drawn is a king}D= {the card drawn is a heart}.Find "probability of eventCOReventDoccurring",P(CUD).

Enter answer either as fraction or as decimal rounded to nearest thousandth (three places after decimal).Examples of correctly entered responses:

11/450.3000.8603/70.571

7. This quarter, there is a 50% chance that Jason will pass Accounting, a 60% chance that he will pass English, and 80% chance that he will pass at least one of these two courses. What is the probability that he will pass both Accounting and English?

8. Question 8 options:

The May 2016 makeup of the US Senate by party affiliation and gender follows:

Male (M)

Female (F)

Total

Democrat (D)

30

14

44

Independent (I)

2

0

2

Republican (R)

48

6

54

Total

80

20

100

Enter probability as a fraction or as a decimal rounded to nearest thousandth (three places).Examples of correctly entered responses:

3/55/110.3000.6500.971

a.P (M D)

b.P(F R)

c.P(MUD)

d.P (MUF)

Use the addition rule to determine the following probabilities:

9 .Enter answer as a decimal rounded to the nearest thousandth (three places after decimal).Examples of correctly entered responses:

a.IfP(E) = 0.5 andP(F) = 0.4 andEandFare mutually exclusive, findP(EF).

b.IfP(E) = 0.4 andP(F) = 0.2 andEandFare mutually exclusive, findP(EUF).

10. A basket contains six red and four blue marbles. Three marbles are drawn at random without replacement.with a tree diagram and (WITHOUT using combinations)determine the probability that:

Enter probability as a fraction or as a decimal rounded to nearest thousandth (three places)

a. all three marbles drawn are red

b.two marbles drawn are red and one is blue (order of selection doesn't matter)

c one marble drawn is red and the other two marbles drawn are blue (order of selection doesn't matter)

c.the first marble randomly drawn is red; the second marble randomly drawn is blue; and the third marble randomly drawn is red (now order of selection DOES matter)

11. A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors (obviously without replacement since one person can't simultaneously fill two committee spots). Enter probability as a fraction or as a decimal rounded to nearest thousandth (three places).Examples of correctly entered responses:=

Using combinations, determine the probability that:

a.at least three freshmen.are selected

b.all four selected are of the same class (order of selection doesn't matter)

c.all four selected are NOT of the same class (order of selection doesn't matter)

d.exactly three of the same class are selected (order of selection doesn't matter)

12. At Faber College, 20% of the students take Finite Math, 30% take History, and 5% take both Finite Math and History. If a single student is chosen at random, find the probability that: Enter answer as a percentage rounded to the nearest tenth

a.the randomly selected student is taking Finite Math given that said student is taking History

b. the randomly selected student is taking History given that said student is taking Finite Math

13. Use expected value calculation method to find the following:

In a European country, 20.0% of the families have 3.0 children, 40.0% have 2.0 children, 30.0% have 1.0 child, and 10.0% have 0.0 children. On average, how many children are there to a family?

Enter answer as a number rounded to the nearest tenth (one place after decimal).Examples of correctly entered responses:

14. A Texas oil drilling company has determined that it costs $25,000 to sink a test well. If oil is hit, the net revenue for the company will be $475,000 (which is $500,000 gross revenue - $25,000 drilling cost). If natural gas is found, the net revenue will be $125,000 (which is $150,000 gross revenue - $25,000 drilling cost). If the probability of hitting oil is 3.00% and of hitting gas is 6.00%, find the expected value of sinking a test well.

Enter answer in dollars rounded to the nearest cent (two places after decimal