## Sample Test

True/False

1. a) Probabilities can never be greater than 1 or less than 0.

b) The sum of probabilities for all experimental outcomes equals 1.

c) The sum of the probabilites of the experimental outcomes in an event must equal 1

d) If two events are independent, they must be mutally exclusive.

Multiple choice

The following event probabilites fo a statistical experiment are utilized in questions 2-4.

P(A)= .60 P(B)= .40

P(A intersect B) =.25

2. P(AUB) is closest to

a. .65

b. .72

c. .79

d. .82

3. P(A|B) is closest to

a. .60

b. .67

c. .74

d. .81

4. P(A^c) is closest to

a. .50

b. .60

c. .70

d. .80

5. Give the conditions for a binomial situation and the setting for a geometric distribution.

6. In which of the following games of chance would you be willing to assume independence of X and Y in making a probability model? Explain you answer in each case.

a. In blackjack, you are dealt two cards and examine the total points X on the cards (face cards count 10 points). You can choose to be dealt another card and compete based on the total points Y on all three cards.

b. In craps, the betting is based on successive rolls of two dice. X is the sum of the faces on the first roll, and Y the sum of the faces on the next roll.

7. Consider a binomial experiment with two trials and p = .4.

a. Draw a tree diagram showing this as a two-trial experiment

b. Compute the probability of one success f(1).

c. Compute f(0).

d. Compute f(2).

e. Find the probability of at least one success.

f. Find the expected value (mean) and standard deviation.