Review For Probability Test

1. Which of the following values cannot be probabilities?

3 50, 1, 1, 2, 0.0123, , , 2

5 3

2. In the New York State Lottery, you have to select six numbers between 1 and 54 inclusive. There are 25,827,154 different possible six number combinations.

What are your chances of winning the grand prize (all six correct numbers) if you buy 100,000 tickets each with distinct number combinations? Round your answer to 3 decimal places.

0.004

3. Assuming that boys and girls are equally likely, a couple had four children one at a time. The first was a boy; the second was a boy; the third was a boy and the forth was also a boy. Now they are expecting their 5th baby. They still don’t know the sex of the baby but they do know that it is not a multiple birth. what is the probability that there fifth baby is also a boy?

0.5

4. An American household is chosen at random and asked how many cars and trucks that household owns. Here are the probabilities as of 1997:

This is a legitimate assignment of probabilities because it satisfies these rules:

(a) all the probabilities are between 0 and 1.(b) all the probabilities are between -1 and 1.(c) the sum of all the probabilities is exactly 1.(d) Both (a) and (c).

D

5. What is the probability that a randomly chosen

household owns more than one motor vehicle?

(a) 0.96 (b) 0.71 (c) 0.26 (d) 0.25

B

6. It is common for public opinion polls to have a confidence level of 95%, meaning that there is a 0.95 probability that the poll results are accurate within the claimed margins of error. If five different organizations conduct independent polls, what is the probability that all five of them are accurate within the claimed margins of error? (Round to 3 decimals)

0.774

7. For Yorktown students, there are only five different restaurants to go for lunch: Wendy’s, Bagel Bakery, Taco Bell, Harris Teeter and Subway. Each restaurant is independent of each other and students can only go one place for lunch. The probability of a student going to Wendy’s is 0.27, Bagel Bakery is 0.32, Taco Bell is 0.12, and Harris Teeter is 0.08.

a.What is the probability of a student going to Subway for lunch?

b.What is the probability of a student going to a “fast food” restaurant for lunch? (Wendy’s or Taco Bell)

.21

.39

8. Decide whether events A and B are mutually exclusive.

A- Being left handed B - Being femaleA- Rolling a dice and getting a 6 B – Rolling a dice and getting an odd

numberA – Being born in July B - Being born in 1990

P(A) = 4/15 and P(B) = 6/15P (A or B) = 10/15

NO

Yes

NO

Yes

9) A bag contains 15 marbles; four are red, five are green, six are yellow. (Answer in decimal form)

– a. If one marble is randomly selected what is the probability that it is not red?

– b. If one is randomly selected, what is the probability that it is red or green?

– c. If one is randomly selected, what is the probability that it is not blue?

11/15=.73

9/15=.6

15/15=1

10. A single playing card is randomly drawn from a standard deck of 52 cards. (Decimal Answers)

a. What is the probability that it is an Ace?

b. What is the probability that it

is a red card?

c. What is the probability that it is a jack or a spade?

d. What is the probability that it

is not a 6 or a diamond?

4/52=.08

26/52=.5

16/52=.31

36/52=.69

Review Game Rules:• One chance per question!• In order to get credit for the

question, you need to show both the set up and the final answer in percent or decimal form!

• First correct Answer gets 2• Second correct Answer gets 1• Answers need to be presented on

the white boards!

11. I What is the probability of rolling two dice

and getting a total of six?

II. What is the probability of getting a total of seven?

III. What is the probability of getting a total of 2 or three?

C

D

A

12. Six cards are randomly drawn from a standard deck without replacement. What is the probability that at least one of them is a

club?Decimal Answer

1-(39/52)(38/51)(37/50)(36/49)(35/48)(34/47)=.84

13. Four firms using the same auditor independently and randomly select a month in which to conduct their annual audits. What is the probability that the months are the same for all four auditors?

Decimal Answer(12/12)(1/12)(1/12)(1/12)=.00058

14. Ten percent of us are left handed. What is the probability that 8 randomly selected people will all be right handed?

Decimal Answer

(.9)^8=.43

15. True or False? If you were to roll a fair dice 1,000 times, the proportion of six’s rolled will be a lot closer to 0.17 than if you were to do it only 5 times.

TRUE!!!!

16. A classic excuse for a missed test is offered by four students who claim that their car had a flat tire. On the makeup test, the instructor asks the students to identify the particular tire that went flat. If they really didn’t have a flat tire and randomly select one that supposedly went flat, what is the probability that they will all select the same tire? Decimal Answer

(4/4)(1/4)(1/4)(1/4)=.016

17. If a couple plans to have eight children, find the probability that they have at least one boy.

Decimal Answer

1-(1/2)^8=.996

18. What is the probability that no two people have the same birthday when the number of randomly selected people is 4????

Decimal Answer(365/365)(364/365)(363/365)(362/365)=.984

19. An employee needs to call any one of five colleagues. Assume that the five colleagues are random selections from a population in which 28% have unlisted numbers. Find the probability that at least one of the five fellow workers will have a listed number.

Decimal Answer1-(.28)^5=.998

20. There is a 0.63 probability that Mobil stock will rise, a 0.75 probability that Gulf stock will rise, and a 0.47 chance that both stocks will rise. Find the probability that neither stock will rise.

.2775

21. A typing pool is made up of five men and five women. If three different typists are randomly selected from the pool, find the probability that at least one of the three is a man. Decimal Answer

1-(5/10)(4/9)(3/8)=.92