Name: ____________________________________
Date: _____________
Probability Review
Section 1 – Theoretical and Experimental Probability
1) What is the difference between Experimental and Theoretical Probability?
__________________________________________________________________
__________________________________________________________________
2) P(Rolling a 4)
3) P(Picking a Club from a standard deck)
1
1
6
4
For # 4 and 5, a spinner like the one shown is used in a game. Determine the
theoretical probability of each outcome if the spinner is equally likely to land on
each section. Express each probability as a fraction and a percent.
4) P(Not Shaded)
5) P(Multiple of 5)
11
16
3
16
Section 2 – Compound Probability
6) What formula should you use for questions that contain Compound Probability?
__________________________________________________________________
7) P(Picking a Jack and Picking a Heart)
3
208
8) P(Rolling a Prime Number and Flipping a Head)
1
4
9) Define probability with replacement ____________________________________
__________________________________________________________________
10) Define probability without replacement _________________________________
__________________________________________________________________
11) Fifteen names are placed in a hat. Ten belong to freshmen and 5 belong to
sophomores. If 2 cards are drawn from the hat one at a time, what is the
probability that the first will be a sophomore and the second will be a freshman?
5
21
12) What is the probability of rolling two dice, getting a number greater than five on
the first roll and a multiple of two on the second roll?
1
12
13) A pizzeria offers 2 choices of crust, 5 cheese toppings, 4 veggie toppings, and 6
choices of meat. The Westwood football teams wants a to order a pizza with one
cheese, one veggie, and one meat topping. What is the probability that they will
choose a thin crust, mozzarella cheese, green peppers, and sausage combination?
1
240
Section 3 – Mutually Exclusive Probability
14) What makes Mutually Exclusive Probability different from Compound
Probability? ______________________________________________________
15) What formula should you use for questions that contain Mutually Exclusive
Probability? ______________________________________________________
16) P(Picking a Face Card or Picking a 7)
17) P(Picking a Vowel or Picking the letter B)
4
3
13
13
18) A single letter is chosen at random from the word WESTWOOD. What is the probability
of picking a W or a T?
3
8
19) Each of the numbers from 1 to 40 is written on a card and placed in a bag. If one card is
drawn at random, what is the probability that the number is a multiple of 5 or a multiple
of 11?
11
40
Section 4 – Counting Outcomes
20) Draw a tree diagram to find the number of different outcomes that can be assembled
using 3 pairs of socks and 4 pairs of sneakers.
12 outcomes
For #21 and 22, find the total number of outcomes for each situation.
21) Joan randomly dials a seven-digit phone number.
10,000,000
22) A winter sweater comes in wool or fleece, with a zipper or crew neck, and in three colors.
12 outcomes
For #23 and 24, find the probability of each event.
23) An eight-sided die is rolled and a coin is tossed. What is the probability of landing on an
even number and getting heads?
1
4
24) Jen and Travis are playing a game that requires each player to roll a number cube and
choose one maker from a bag without looking that contains one red, one blue, one green,
and two yellow makers. The player that rolls an even number and chooses a yellow
marker is the winner. What is the probability of a player rolling an even number and
drawing a yellow marker without looking?
1
5
Section 5 – Permutations and Combinations
25) Give your own definition of Permutations. ______________________________
_________________________________________________________________
26) Give your own definition of Combinations. ______________________________
__________________________________________________________________
27) How many ways can 3 cookie batches be chosen out of 6-prize winning batches?
28) How many ways can 30 students be arranged in a 4-student line?
657, 720
29) A local restaurant specializes in simple and tasty meals.
a. How many sandwiches are possible if the restaurant lets you build a sandwich by
choosing any 4 of 10 sandwich ingredients?
210
b. If there are 6 soups to choose from, how many soup and build-a-sandwich
specials are possible?
1
1260
30) In a raffle, 5 winners get to choose from 5 prizes, starting with the first name drawn. If 87
people entered the raffle, how many ways can the winners be arranged?
4,433,982,840