Question 1. The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Business?
A. 0.7800
B. 0.8200
C. 0.8300
D. 0.9200
Question 2. Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?
A. $0.00
B. -$0.40
C. -$1.00
D. -$0.50
Question 3. Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?
A. $1.00
B. $0.00
C. $3.00
D. -$1.00
Question 4. Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?
A. 12
B. 22
C. 24
D. 26
Question 5. A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?
A. 2/11
B. 3/11
C. 5/14
D. 3/14
Question 6. Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?
A. 2
B. 4
C. 3
D. 5
Question 7. If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails?
A. ½
B. 2/3
C. 3/4
D. 4/9
Question 8. Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places).
A. 0.250
B. 0.490
C. 0.240
D. 0.160
Question 9. A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?
A. 32/132
B. 27/66
C. 50/132
D. 82/132
Question 10. On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?
A. 1/5
B. 1/6
C. 1/4
D. 2/5
Question 11. Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.
A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.
B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.
C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.
D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.
Question 12. Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town.
A. 0.345
B. 0.425
C. 0.587
D. 0.592
Question 13. Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?
A. 8
B. 6
C. 5
D. 4
Question 14. A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man's expected value for the insurance policy?
A. $139,916
B. -$41
C. $84
D. -$124
Question 15. The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.
112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000
140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000
A. 0.4
B. 0.6
C. 0.66
D. 0.7
Question 16. If you flip a coin three times, the possible outcomes are HHH, HHT, HTH,
HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?
A. 4/9
B. 5/6
C. 7/8
D. 5/8
Question 17. A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain.
A. 2/6
B. 3/6
C. 4/6
D. 5/6