1) A person pays $3 to play a certain game by rolling a single die once.If a 1, 2, or 3 comes up, the person wins nothing.If, however, the player rolls a 4, 5, or 6, he or she wins the difference between the number rolled and $3.Find the expectation for this game.Is the game fair?

Find the gain and probability for each roll:

Roll

1

2

3

4

5

6

GainX

3

3

1

Probability P(X)

E(X) = += _______

Thus, in the long run, a player will _______ money and the game (is) / (is not) fair.

2) If 20% of children were reported to want a particular toy, use the table to find the probability that

a.exactly 4 of 7 children want that toy.

b.at most 3 of 7 children want that toy.

c.at least 4 of 7 children want that toy.

Solution:

3) In a survey, 3 of 4 students said the courts show "too much concern" for criminals.Find the probability that at most 3 out of 7 randomly selected students will agree with this statement.

Solution:

4) Classify each of the situations as binomial or not.

a.Roll a standard die 200 times.

b.Survey 100 shoppers asking for their favorite exercise shoe brand.

c.Survey 100 teenagers asking if they play the video game Halo.

d.Ask 300 viewers if they recall seeing a Coca Cola commercial during a particular show?

e.Test four brands of aspirin to see which brands are effective.

Solution:

5) A study concerning the number of trips of five nights or more that American adults take per year showed that 6% did not take any trips lasting five nights or more, 70% take one trip lasting five nights or more, 20% take two trips lasting five nights or more, 3% take three trips lasting five nights or more, while only 1% take four trips lasting five nights or more.Fill in the chart below and find the mean number of trips American adults take per year.

Number of trips, X

0

1

2

3

4

Probability, P(X)

______________________________________ = ________

Thus, the mean number of trips lasting more than five nights or more per year taken by American adults is __________.