Probability
Permutations/
Combinations/Counting Principle
Combinations/Counting Principle
Dice
Cards
Word Problems
Two-Way Frequency Tables/Venn Diagrams
Factorials
100
A coin is flipped three times. What is the probability of getting all heads?
(1/2)(1/2)(1/2)=
1/8 or 12.5%
100
How many 4-digit codes can be made using the digits 1-7, no repetition.
7*6*5*4=840
100
The odds of rolling a 3 on 6 sided dice.
1:5
100
In a standard deck of cards, what is the probability of pulling a diamond, replacing it, and pulling a 9?
13/52*4/52=52/2704
100
A deli offers 6 sandwiches, 6 drinks, and 4 desserts. How many different combinations can you make if you choose one from each category?
144
100
What is the probability that a randomly chosen student eats breakfast and is aged 10 - 13?
40/90
4/9=44.44%
100
What is 7!
5040
200
Jim rolls a number cube. What is the probability of rolling a 5 or 6. (Make sure you simplify)
1/6+1/6=2/6
1/3 or 33.33%
200
How many distinguished permutations can you have with the letters in WINNIPEG?
(8!)/(2!2!)=10,080
200
What is the probability of rolling an even number, a number larger than 5, and an odd number when rolling a dice 3 times?
3/6*1/6*3/6=9/216
1/24 or 4.17%
200
With a standard deck of cards, what is the probability of pulling a black card, putting it back, and then pulling a diamond?
26/52*13/52=338/2704
1/8 or 12.5%
200
A building has 10 doors. How many ways can you enter and exit the building if you cannot exit from the same door you entered?
10*9=90
200
Given a students eats breakfast, what is the probability that they are aged 14-17?
12/47 or 25.53%
200
What is
(8!)/(5!)
336
300
A cooler contains 5 cans of Coke, 6 cans of Dr. Pepper, and 4 cans of Sprite.
What is the probability of selecting a Coke and then a Sprite with replacement? (Simplify)
5/15*4/15=20/225
4/45 or 8.89%
300
How many ways can you make a starting basketball line-up of 5 players from a team of 12 players?
12 C 5 = 792
300
A die is rolled. What is the probability that the number is even or less than 4?
3/6+3/6-1/6=5/6
5/6 or 83.33%
300
The probability of picking a 7 and a heart in a deck of cards?
1/52 or 1.92%
300
A class has 10 students in it, 4 boys and 6 girls. What is the probability that you will draw 3 boys names out of a hat. (without replacement)
(4*3*2)/(10*9*8)=24/720
1/30 or 3.33%
300
What is the probability that a randomly chosen person likes football and likes chocolate?
10/72=5/36 or 13.89%
300
What is
(10!)/(2!4!)
75,600
400
8 cards are labeled with the numbers 1 through 8. A card is chosen and then a second card is chosen. What is the probability that both cards will be even numbers?
4/8*3/7=12/56
3/14or 21.43%
400
How many ways can we deal 5 diamonds from just the diamonds in a standard deck of cards?
13 C 5 = 1287
400
The probability of rolling a 2 and a prime number with two dice.
1/6*3/6=3/36
1/12 or 8.33%
400
What is the probability of a person drawing a king given that it is a club?
1/13 or 7.69%
400
A box of candy has 20 jelly beans. There are 10 red jelly beans, 4 green jelly beans, 3 purple jelly beans, and 3 yellow jelly beans. You pull out a red jelly bean, eat it, and select another jelly bean. What’s the probability that you pulled a red jelly bean and then a second red jelly bean?
P(red, then red)
10/20*9/19=90/380
9/38 or 23.68%
400
40 people were asked whether they like coffee, tea or both. 9 people liked neither drink. 24 people liked coffee. 17 people liked tea. Complete the Venn diagram. What is the probability of a person who likes tea given they like coffee.
10/24 or 41.67%
400
How many ways can you arrange 5 people in a row?
120
500
If you roll a die five times, what is the probability of getting at least one 6?
P(at least one six)=1-P(no six)
P(no six) = P(all not six) = (5/6)5 = 0.401878
P(at least one six)= 1-0.401878 = 0.598122
59.81%
500
How many ways can you choose a dance team of 2 ballet dancers and 3 hip-hop dancers from a group of 8 ballet dancers and 7 hip-hop dancers?
(8 C 2)(7 C 3) = 980
500
What is the probability of getting 10 with two dices? (All six sided)
3/36
1/12 or 8.33%
500
What is the probability of drawing a face card from a normal deck of cards. And then drawing another face card from the deck given that the first card was not put back into the deck?
12/52*11/51=132/2652
11/221 or 4.98%
500
A bag contains 5 blue marbles, 6 red marbles, 2 yellow marbles, and 7 green marbles. Without replacement, find the probability of pulling a green marble, a second green marble, and then a red marble.
7/20*6/19*6/18=252/6840
7/190 or 3.68%
500
The Venn diagram alongside shows the number of people in a sporting club who play tennis (T) and hockey (H). What is the probability of a student playing hockey, given that they do not play tennis.
26/33or78.79%
500
What is 8!3!
241,920
600
If a couple plans to have three children, what is the probability that they will have at least one girl?
P(at least one girl)=1-P(no girls) = 1 – P(all boys)
P(all boys)= (1/2)3 = 0.125
P(at least one girl) = 1 - 0.125 =0.875
87.5%
600
A password is 3 capital letters followed by 3 digits. How many possible passwords have the order consonant, vowel, consonant, followed by the digits? Repetition is possible.
(21)(5)(21)(10)(10)(10)=
2,205,000
600
You roll a 10-sided die. Find the odds in favor of rolling a perfect square number.
3:7
600
How many possible 8 card hands are possible that contain the following:
6 black cards and 2 red face cards
(26C6)(6C2)=
3,453,450
600
A class has 3 boys who play the sax, 2 boys who play the drums, and 4 boys who don't play an instrument. The class also has 2 girls who play the sax, 1 girls who plays the drums, 3 girls who play the flute, and 5 girls who don't play an instrument.
If you randomly select a girl from the class, what is the probability that she plays the sax or the flute?
2/11+3/11=
5/11 or 45.45%
600
Draw a Venn Diagram. In a class of 40 students, 25 are taking Algebra 2 and 18 are taking Spanish. If 8 students are taking both. What is the probability that a student is not taking either class?
5/40 =1/8 or 12.5%
600
What is
(2!5!)/(3!)*6!
28,800