Additional T102 Probability Problems
1. A spinner can land on four different colors: red-R, green-G, yellow-Y and blue-B. If we assume the spinner is not divided equally, which of the following probability assignments would have to be rejected and why?
a) P(R) = .15 P(G) = -.35 P(Y) = .50 P(B) = .70
b) P(R) = .32 P(G) = .28 P(Y) = .24 P(B) = .30
c) P(R) = .26 P(G) = .14 P(Y) = .30 P(B) = .30
2. A thumbtack is tossed 1,000 times with the following outcome frequencies:
point down = 389 and point up = 611. Compute the approximate empirical probability for each outcome. Does each outcome appear equally likely?
3. An experiment consists of tossing a regular die with faces number 1 through 6. Consider the events E: Obtain an even numberF: Obtain a prime number
G: Obtain an odd number
a) Find P(E
F) and P(E) + P(F)
b) Find P(E 
G) and P(E) + P(G)
4. If we select a card from an ordinary deck of 52 cards and then select another card without replacing the first, find the probability of selecting 2 face cards.
5. Box 1 contains 2 red marbles and one blue marble. Box 2 contains one green, 2 yellow and one red marble. Consider the experiment of selecting one marble from the first box and one from the second.
a) Sketch a probability tree. Show all possible outcomes and their probabilities
b) What is the probability of selecting two red marbles?
c) What is the probability of selecting at least one red marble?
6. An experiment consists of tossing a coin three times and recording the sequence of heads and tails. For each event described, find its probability
a) A: More than one head P(A) =
b) B: An even number of heads (i.e. 0 or 2) P(B) =
c) C: A head on the last toss P(C) =
7. A spinner has three letters on it: a, b, and c. For any spin the letter b is twice as likely to occur as the letter a, and the letter c is three times as likely to occur as letter a. Find the simple event probabilities for the experiment of spinning the spinner once.
8. The probability that a first proposal passes is 3/7. What are the odds in favor of the first proposal passing?
9. a) If you flipped a fair coin 9 times and got 9 heads, what would be the probability of getting a head on the next toss?
b) If you rolled a fair die 5 times and got the numbers 1, 2, 3, 4, and 5, what would be the probability of rolling a 6 on the next turn.
10. On a certain street there are three traffic lights. At any given time, the probability that a light is green is 30%. What is the probability that a person will hit first two green lights and then a red light?
11. An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find the probability that the sum is 2, 3, or 12.
12. The probability of winning a certain raffle is 1/600. Find the odds against winning.
13. A consumer buys a package of 5 flashbulbs, not knowing that 1 of the bulbs is bad. List the outcomes in the sample space if 2 bulbs are selected randomly and then find the probabilities of the following events.
a) Both bulbs are good b) One of the bulbs is bad
14. A game consists of the following: a single fair die is rolled and you are paid back the number of dollars corresponding to the number of dots facing up.
a) What is the expected value of this game?
b) If you pay $4.00 to play the game, is it a fair game?
15. In a horse race, how many different finishes are possible among the first 3 places if 10 horses are running? (exclude ties)
16. Eight distinct points are selected on the circumference of a circle. How many triangles can be drawn using these points as vertices?
17. The probability of living to age 65 is 7/10. Find the odds in favor of living to age 65.
18. A box contains 4 black and 2 purple marbles. Consider the experiment of randomly selecting a marble from the box, and then selecting a second marble, without replacing the first. Determine the probabilities of the following events.
a) Selecting 2 black marble
b) Selecting 2 purple marbles
c) Selecting one black and 1 purple marble.
19. If there are 25 applicants for a job, in how many ways can a manager select a first, second and third choice candidate for the position?
20. If there are 25 applicants for a job, in how many ways can a manager choose three individuals to be interviewed?
ANSWERS
1. a and b 2. 0.389, 0.611, no 3. a) 5/6, 1 b) 1, 1 4. 11/221 5. 1/6, ¾
6. a) ½ b) ½ c) ½ 7. P(a) = 1/6, P(B) = 1/3, P(c) = ½ 8. 3 : 4 9. a) ½ b) 1/6
10. 0.63 11. 1/9 12. 599 : 1 13. a) 3/5 b) 2/5 14. a) $3.50 b) No
15. 720 16. 56 17. 7 : 3 18. a) 2/5 b) 8/15 c) 1/15
19. P(25,3) = 25 x 24 x 23 = 13,800 20. C(25,3) = 2300