Basics
Rules of Probability
Tables and Probability
Multiplication Rule
Counting Rules
100
If you flip a fair coin three times, what is the probability of the coin landing on tails exactly twice?
3/8
100
Suppose that A and B are mutually exclusive events such that P(A)=0.25 and P(B)=0.40.
Determine P(A or B)
0.65
100
P(Y_1)
18/62
100
If you roll a fair die 3 times, what is the probability of the die landing on an even number each time?
(1/2)^3=1/8
100
Simplify: 7!
5040
200
If you randomly draw one card from a deck of cards, what is the probability of drawing not a heart?
39/52 or 3/4
200
If you randomly draw one card from a deck of cards, what is the probability of drawing a King or a Spade?
16/52
200
P(Y_2andW_3)
4/62
200
A class consists of 10 male and 10 female students. If four students are selected at random, without replacement, what is the probability that all four are male?
(10/20)(9/19)(8/18)(7/17)=56/1292
200
Simplify: 6 nPr 2
30
300
A bowl contains 12 poker chips - 3 red, 4 white, and 5 blue. If you draw two chips without replacement from the bowl, what is the probability of drawing two blue chips?
(5/12)(4/13)=20/156
300
Suppose that A and B are events such that P(A)=0.84, P(B)=0.46, and P(A&B)=0.38. Determine P(A or B).
0.92
300
P(W_1 or Y_2)
33/62
300
Next weekend you are expecting a visit from Bonnie and Clyde. The probability that Bonnie will show up is 0.4, whereas the probability that Clyde will show up is 0.8. What is the probability that at least one of them will visit you next weekend?
1-(.6)(.2)=.88
300
How many different groups of 4 students are possible if there are 12 students to choose from?
495
400
If a balanced die is rolled 3 times, what is the probability of rolling the same number all 3 times?
6/216=1/36
400
A document about school enrollment tells us that 85.3% of students attend public school, 27.9% attend college, and 20.1% of students attend public schools and college. What percentage of students attend either public school or college?
93.1%
400
P(Y_1 |W_2)
11/41
400
Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is equally likely to pick any of the 8 flavors. What is the probability that each child orders a different ice cream type
(7/8)(6/8)(5/8)=105/256
400
Suppose a license plate is three numbers followed by three letters. If there are no limitations on the numbers, but the letters can not be repeated, how many different license plates are possible?
15,600,000
500
Explain what is wrong with the following argument: When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. Therefore, the probability is 1/11 that the sum is 12.
More than one way to roll the sums of 3-11
500
A jar contains 7 marbles that are identical except for color: four are red and three are green. A game is played in which one marble at a time is taken out of the jar (and not replaced). The game ends when either three red marbles or two green marbles have been removed from the jar. What is the probability that the game will end on the third draw?
72/210 or 12/35
500
In the experiment of rolling two dice, what is the probability of rolling a sum of 8, given you roll two even numbers.
3/9 or 1/3
500
A city has three major newspapers, Times, Herald, and Examiner. 47% of households get the Times, 33% of households get the Herald, and 35% get the Examiner. If a household in the city is selected at random, determine the probability that it gets at least 1 of the 3 newspapers.
1-(.53)(.67)(.65)=.77
500
Suppose the Chapter 4 Quiz consists of 10 questions. The first five are true/false, and the next five are Multiple Choice with options A-D. How many different ways are there to answer the questions on the test?
32,768