1.
There are 9 beads in a bag. 3 beads are red, 3 beads are blue, and 3 beads are black. If two beads are chosen at random, what is the probability that they are both blue?
A. 1/81 B. 1/12 C. 2/9 D. 1/3 E. ¼
Method #1: P(2 blue) = 3/9 ∙ 2/8 = 1/12 Since there are 3 out of 9 on the first draw and then 8 left to choose from you have to multiply by 2/8.
Method 2: The condition is that you want 2 of the 3 blue beads in the bag. This is set up as C(3,2) = s.
Working this out gives you 3. To solve for s + f, you set up the condition C(9,2). Working this out 𝒔 gives you 36. The probability formula of P(s) = 𝒔+𝒇
would be 3/36 = 1/12, same as Method 1!
2.
A letter is randomly selected from the word Mississippi. What is the probability that the letter will be an s?
A. 1/11 B. 3/10 C. 4/11 D. ¼ E. 1/3
The word Mississippi has 11 letters, 4 of which are s. So the probability is 4/11.
3. A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?
A. 15/28 B. ¼ C. 9/16 D. 1/32 E. 1/16
P(not blue) on the first draw is 6/8. After one is drawn the P(not blue) is 5/7. Solve (6/8 ∙ 5/7).
4. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2?
A. 1/2 B. ¼ C. 1/6 D. 1/12 E. 1/3
On the coin toss the probability is ½. For the roll of the dice, the probability is 2/6 because you would be happy with either a 1 or a 2. Solve (1/2 ∙ 2/6).
5. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?
A. 21/50 B. 3/13 C. 47/50 D. 14/15 E. 1/5
This question involves what is called a “complement an event”. We have not learned this and it will not be on the test, but if you are interested…… The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A. What we do is find out the P(not blue) which equals (3/10 ∙ 2/9). That answer is 1/15. The Complement Rule states: Given the probability of an event, the probability of its complement can be found by subtracting the given probability from 1….so 1 -
1/15 = 14/15.
6. A fair, six-sided die is rolled. What is the probability that the number will be odd?
A. ¼ B. ½ C. 1/3 D. 1/6 E. 1/5
There are 3 odd numbers out of 6, so 3/6 = ½.

7. A letter is randomly select from the word studious. What is the probability that the letter be a U?
A. 1/8 B. ¼ C. 1/3 D. ½ E. 3/8
There are 8 letters in the word studious, with 2 u’s, therefore the P (u) = 2/8, or ¼.
8. A bag contains 2 red beads, 2 blue beads, and 2 green beads. Sara randomly draws a bead from the bag, and then Victor randomly draws a bead from the bag. What is the probability that Sara will draw a red marble and
Victor will draw a blue marble?
A. 2/13 B. 1/5 C. 1/3 D. 1/10 E. 2/15
There are 6 total beads. When Sara draws the probability of drawing a red is 2/6 or 1/3. When Victor draws (and assuming there is no replacement) the probability of him drawing a blue is 2/5. Multiply 1/3 ∙
2/5 = 2/15.
9. If two fair, six-sided dice are rolled, what is the probability that the sum of the numbers will be 5?
A. 1/6 B. ¼ C. 1/36 D. 1/18 E. 1/9
There are 36 different combinations that we could get if we roll 2 dice. We would be happy with 4: (1,4),
(4,1), (2,3) and (3,2). So we have a probability of 4/36, or 1/9.
10. If four fair coins are tossed, what is the probability of all four coming up heads?
A. ¼ B. 1/6 C. 1/8 D. 1/16 E. 1/32
Each coin has a ½ probability of coming up heads, therefore the probability of all four coming up heads is represented by the equation 1/2∙1/2∙1/2∙1/2, which equals 1/16.
11. The probability that a certain event will occur is 5/9. What is the probability that the event will NOT occur?
A. 5/9 B. 4/9 C. 2/9 D. ¼ E. ½ 𝒔
If we think about the probability formula of P(s) = 𝒔+𝒇
with this problem, we see that the successes and failures add up to 9. Therefore, we subtract the successes (5) from the total (9) and get 4.
The P (not occurr) = 4/9.
12. A certain bag contains red, blue, yellow, and green marbles. If a marble is randomly drawn from the bag, the probability of drawing a blue marble is .2, the probability of drawing a red marble is .3, and the probability of drawing a yellow marble is .1. What is the probability of drawing a green marble?
A. .5 B. .6 C. .2 D. .4 E. .3
Remember that a probability of 100% = 1, so 1 - .2 - .3 - .1 = .4.
13. A bag contains 3 red marbles, 3 blue marbles, and 3 green marbles. If a marble is randomly drawn from the bag and a fair, six-sided die is tossed, what is the probability of obtaining a red marble and a 6?
A. 1/15 B. 1/6 C. 1/3 D. ¼ E. 1/18
3/9 ∙ 1/6 = 3/54 = 1/18

14. A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?
A. 1/6 B. 1/5 C. ¼ D. 2/3 E. ½
We have not learned this and it will not be on the test, but if you are interested……this probability involves addition. The first event has a probability of 1/6 and the second a probability of 3/6, so we add them. 1/6 + 3/6 = 4/6 = 2/3. This is done when we have a probability with an either/or condition.
15. At a certain business school, 400 students are members of the sailing club, the wine club, or both. If 200 students are members of the wine club and 50 students are members of both clubs, what is the probability that a student chosen at random is a member of the sailing club?
A. ½ B. 5/8 C. ¼ D. 3/8 E. 3/5
If there are 400 students and 200 are in the wine club which leaves 200 students. The two clubs share 50 members, so 200 - 50 = 150. There are 150 members in the sailing club. The probability that a student is in the sailing club is 150/400 = 5/8. (I am assuming they mean the sailing club only.)
16. A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?
A. 1/3 B. ½ C. 1/8 D. ¼ E. 1/5
There are 6 marbles total, so the probability of the first draw is 2/6, and assuming no replacement, the probability of the second draw is 1/5. We multiply 2/6 ∙ 1/5 = 2/30 = 1/15.
17. There are five students in a study group: two finance majors and three accounting majors. If two students are chosen at random, what is the probability that they are both accounting students?
A. 3/10 B. 2/5 C. 1/5 D. 3/5 E. 4/5
3/5 ∙ 2/4 = 6/20 = 3/10.
18. Seven beads are in a bag: three blue, two red, and two green. If three beads are randomly drawn from the bag, what is the probability that they are not all blue?
A. 5/7 B. 23/24 C. 6/7 D. 34/35 E. 8/13
First figure out the probability that they are all blue. P (blue) = 3/7 ∙ 2/6 ∙ 1/5 = 6/210 = 1/35. (This is assuming no replacement.) Then subtracting from 1 – 1/35 = 34/35, which is the failures and would be not all blue.
19. A bag has six red marbles and six blue marbles. If two marbles are drawn randomly from the bag, what is the probability that they will both be red?
A. ½ B. 11/12 C. 5/12 D. 5/22 E. 1/3
This is assuming no replacement, so on the first draw the probability is 6/12, but the second draw is 5/11.
We multiply the two to get 30/132 = 5/22.