MGF 1107/ CLASS EXAMPLES/ PROBABILITY

1. The governor has narrowed his choices for a new agency director to five finalists:

Kathy Johnson Democrat

Mario Cifuentes Republican

Bill Baird Republican

Cindy Hawkins Republican

Patrick Snyder Republican

The governor has no preference for one over the other; in other words, each has an equally likely chance of being chosen. Find the probability that:

a) Bill Baird is chosen

b) Cindy Hawkins is chosen

c) Bill Baird or Cindy Hawkins is chosen

d) a female is chosen

e) a Republican is chosen

f) a female Republican is chosen

g) a Democrat or Republican is chosen

h) an independent is chosen

2. Past records show that the probability that a senator votes to confirm a nominee to the federal judiciary is .88. What is the probability that the senator votes to reject a nominee to the federal judiciary?

3. The probability that an FIU student voted for the incumbent for Student Government President is .09 and the probability that he or she voted for the lone challenger was .06. What is the probability that an FIU student didn’t vote at all in the election?

4. Suppose a Republican is three times more likely to support a constitutional amendment to ban flag burning than to oppose it. What is the probability that a Republican supports the amendment?

5. Suppose African-Americans are one-fourth as likely to support a Republican candidate than a Democratic candidate. What is the probability that an African-American supports a Republican candidate?

6. The staff of a Senator is 75% male and 25% female. 60% of the staff has leaked a story to the news media. Find the probability that a staff member:

a) is female and has leaked a story.

b) is female and hasn’t leaked a story.

c) is male and has leaked a story.

d) is male and hasn’t leaked a story.

7. To see the mayor in his office without an appointment, one must get past the receptionist and the mayor’s personal secretary. The probability that a visitor gets past the receptionist is ½. The probability that a visitor gets past the mayor’s secretary is ¼. What is the probability that a visitor gets to see the mayor?

8. Records show that if it rains on Election Day, voter turnout will be 30%. If it doesn’t rain, voter turnout will be 50%. Next Tuesday is Election Day and there is a 60% chance of rain. What is the expected turnout on Tuesday?

9. The variable X can have only the values 3, 6, 7, 0, and –2 with the following probabilities.

X	3	6	7	0	-2
Probability	.2	.15	.1	.3	.25

What is the expected value of X?

10. A school board member pays her staff according to the following salary matrix.

	No prior experience	Prior experience
Bachelor degree	$40,000	$50,000
Graduate degree	$45,000	$55,000

If 70% of her staff have bachelor degrees and 40% have prior experience, what is the expected salary of one of her staff members?