# MATHEMATICS

1. In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth.A. 0.384 B. 0.380 C. 0.373D. 0.370

P(accident) = 220 / (220 + 370) = 0.373

2. 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

P(at least one head) = (Number of combinations with one or more H) / (Total number of combinations)

P(at least one head) = 7 / 8

3. Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

1^{st} deal: 14 red and 6 black P(red) = 14/20 = 0.70

2^{nd} deal: 20 red and 10 black P(red) = 20/30 = 0.67 < 0.70

4. 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

E(2) = np = 32(1/8) = 4

5. 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. 25/66C. 50/132 D. 82/132

P(woman) = 50 / (50 + 82) = 50/132 = 25/66

6. If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

A. 1/8 B. 3/8 C. 5/8 D. 6/8

P(two consecutive H) = (Number of combinations with HH) / (Total number of combinations)

P(two consecutive H) = 3/8

7. 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

E(x) = (1/1000)($500) – 1 = $0.50 – $1 = -$0.50

8. 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. 1/2 B. 2/3 C. 3/4 D. 4/9

P(at least 2 T) = (Number of combinations with 2 or more T) / (Total number

of combinations)

P(at least 2 T) = 4/8 = ½