Probability measures how likely an event is to happen. To find the probability of an event when all outcomes are equally likely, divide the number of favorable outcomes by the total number of possible outcomes. Probability can be expressed as a fraction, decimal, or percentage, and it ranges from 0 (impossible) to 1 (certain). Practice calculating probability using marbles, coin tosses, and six-sided dice below.
Notes
\(\text{Probability}=\displaystyle \frac{\text{Successful Events}}{\text{Total Events}}\)
Practice Questions
\(\textbf{1)}\) There is a box of marbles. There are 12 red, 7 green and 11 blue marbles. You select 1 marble.
What is the probability of the marble being green?
The answer is \(\frac{7}{30}\approx23.3\%\)
Total marbles: \(12+7+11=30\)
Green marbles: \(7\)
\(\,\,\,\,\,\,P(\text{green})=\frac{7}{30}\)
\(\,\,\,\,\,\,\frac{7}{30}\approx0.2333\)
\(\,\,\,\,\,\,\approx23.3\%\)
Total marbles: \(12+7+11=30\)
Green marbles: \(7\)
\(\,\,\,\,\,\,P(\text{green})=\frac{7}{30}\)
\(\,\,\,\,\,\,\frac{7}{30}\approx0.2333\)
\(\,\,\,\,\,\,\approx23.3\%\)
\(\textbf{2)}\) There is a box of marbles. There are 12 red, 7 green and 11 blue marbles. You select 1 marble.
What is the probability of the marble being blue?
The answer is \(\frac{11}{30}\approx36.7\%\)
Total marbles: \(12+7+11=30\)
Blue marbles: \(11\)
\(\,\,\,\,\,\,P(\text{blue})=\frac{11}{30}\)
\(\,\,\,\,\,\,\frac{11}{30}\approx0.3667\)
\(\,\,\,\,\,\,\approx36.7\%\)
Total marbles: \(12+7+11=30\)
Blue marbles: \(11\)
\(\,\,\,\,\,\,P(\text{blue})=\frac{11}{30}\)
\(\,\,\,\,\,\,\frac{11}{30}\approx0.3667\)
\(\,\,\,\,\,\,\approx36.7\%\)
\(\textbf{3)}\) There is a box of marbles. There are 12 red, 7 green and 11 blue marbles. You select 1 marble.
What is the probability of the marble being red?
The answer is \(\frac{12}{30}=\frac{2}{5}=40\%\)
Total marbles: \(12+7+11=30\)
Red marbles: \(12\)
\(\,\,\,\,\,\,P(\text{red})=\frac{12}{30}\)
\(\,\,\,\,\,\,\frac{12\div6}{30\div6}=\frac{2}{5}\)
\(\,\,\,\,\,\,\frac{2}{5}=0.4=40\%\)
Total marbles: \(12+7+11=30\)
Red marbles: \(12\)
\(\,\,\,\,\,\,P(\text{red})=\frac{12}{30}\)
\(\,\,\,\,\,\,\frac{12\div6}{30\div6}=\frac{2}{5}\)
\(\,\,\,\,\,\,\frac{2}{5}=0.4=40\%\)
\(\textbf{4)}\) There is a box of marbles. There are 12 red, 7 green and 11 blue marbles. You select 1 marble.
What is the probability of the marble being yellow?
The answer is \(\frac{0}{30}=0\%\)
Total marbles: \(12+7+11=30\)
Yellow marbles: \(0\)
\(\,\,\,\,\,\,P(\text{yellow})=\frac{0}{30}\)
\(\,\,\,\,\,\,=0=0\%\)
This is an impossible event.
Total marbles: \(12+7+11=30\)
Yellow marbles: \(0\)
\(\,\,\,\,\,\,P(\text{yellow})=\frac{0}{30}\)
\(\,\,\,\,\,\,=0=0\%\)
This is an impossible event.
\(\textbf{5)}\) There is a bag with 5 red marbles, 3 blue marbles, and 2 green marbles. You select 1 marble. What is the probability of selecting a red marble?
The answer is \(\frac{1}{2}=50\%\)
Total marbles: \(5+3+2=10\)
Red marbles: \(5\)
\(\,\,\,\,\,\,P(\text{red})=\frac{5}{10}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
Total marbles: \(5+3+2=10\)
Red marbles: \(5\)
\(\,\,\,\,\,\,P(\text{red})=\frac{5}{10}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
\(\textbf{6)}\) There is a bag with 5 red marbles, 3 blue marbles, and 2 green marbles. You select 1 marble. What is the probability of selecting a red or blue marble?
The answer is \(\frac{4}{5}=80\%\)
Total marbles: \(5+3+2=10\)
Red or blue marbles: \(5+3=8\)
\(\,\,\,\,\,\,P(\text{red or blue})=\frac{8}{10}\)
\(\,\,\,\,\,\,=\frac{4}{5}=80\%\)
Total marbles: \(5+3+2=10\)
Red or blue marbles: \(5+3=8\)
\(\,\,\,\,\,\,P(\text{red or blue})=\frac{8}{10}\)
\(\,\,\,\,\,\,=\frac{4}{5}=80\%\)
\(\textbf{7)}\) There is a bag with 5 red marbles, 3 blue marbles, and 2 green marbles. You select 1 marble. What is the probability of NOT selecting a green marble?
The answer is \(\frac{4}{5}=80\%\)
Total marbles: \(5+3+2=10\)
Marbles that are not green: \(5+3=8\)
\(\,\,\,\,\,\,P(\text{not green})=\frac{8}{10}\)
\(\,\,\,\,\,\,=\frac{4}{5}=80\%\)
Total marbles: \(5+3+2=10\)
Marbles that are not green: \(5+3=8\)
\(\,\,\,\,\,\,P(\text{not green})=\frac{8}{10}\)
\(\,\,\,\,\,\,=\frac{4}{5}=80\%\)
\(\textbf{8)}\) A box contains 4 yellow marbles, 6 purple marbles, and 10 orange marbles. You select 1 marble. What is the probability of selecting a purple marble?
The answer is \(\frac{3}{10}=30\%\)
Total marbles: \(4+6+10=20\)
Purple marbles: \(6\)
\(\,\,\,\,\,\,P(\text{purple})=\frac{6}{20}\)
\(\,\,\,\,\,\,=\frac{3}{10}=30\%\)
Total marbles: \(4+6+10=20\)
Purple marbles: \(6\)
\(\,\,\,\,\,\,P(\text{purple})=\frac{6}{20}\)
\(\,\,\,\,\,\,=\frac{3}{10}=30\%\)
\(\textbf{9)}\) A box contains 4 yellow marbles, 6 purple marbles, and 10 orange marbles. You select 1 marble. What is the probability of selecting a yellow or purple marble?
The answer is \(\frac{1}{2}=50\%\)
Total marbles: \(4+6+10=20\)
Yellow or purple marbles: \(4+6=10\)
\(\,\,\,\,\,\,P(\text{yellow or purple})=\frac{10}{20}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
Total marbles: \(4+6+10=20\)
Yellow or purple marbles: \(4+6=10\)
\(\,\,\,\,\,\,P(\text{yellow or purple})=\frac{10}{20}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
\(\textbf{10)}\) A box contains 4 yellow marbles, 6 purple marbles, and 10 orange marbles. You select 1 marble. What is the probability of selecting a yellow, purple, or orange marble?
The answer is \(1=100\%\)
Total marbles: \(4+6+10=20\)
Favorable outcomes: \(4+6+10=20\)
\(\,\,\,\,\,\,P(\text{yellow, purple, or orange})=\frac{20}{20}\)
\(\,\,\,\,\,\,=1=100\%\)
This is a certain event.
Total marbles: \(4+6+10=20\)
Favorable outcomes: \(4+6+10=20\)
\(\,\,\,\,\,\,P(\text{yellow, purple, or orange})=\frac{20}{20}\)
\(\,\,\,\,\,\,=1=100\%\)
This is a certain event.
\(\textbf{11)}\) You flip a fair coin one time. What is the probability of getting heads?
The answer is \(\frac{1}{2}=50\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(\text{heads})=\frac{1}{2}=50\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(\text{heads})=\frac{1}{2}=50\%\)
\(\textbf{12)}\) You flip a fair coin one time. What is the probability of getting tails?
The answer is \(\frac{1}{2}=50\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(\text{tails})=\frac{1}{2}=50\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(\text{tails})=\frac{1}{2}=50\%\)
\(\textbf{13)}\) You flip a fair coin one time. What is the probability of getting either heads or tails?
The answer is \(1=100\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(2\)
\(\,\,\,\,\,\,P(\text{heads or tails})=\frac{2}{2}\)
\(\,\,\,\,\,\,=1=100\%\)
Possible outcomes: Heads, Tails.
Total outcomes: \(2\)
Favorable outcomes: \(2\)
\(\,\,\,\,\,\,P(\text{heads or tails})=\frac{2}{2}\)
\(\,\,\,\,\,\,=1=100\%\)
\(\textbf{14)}\) You roll a fair six-sided die one time. What is the probability of rolling a 4?
The answer is \(\frac{1}{6}\approx16.7\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Total outcomes: \(6\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(4)=\frac{1}{6}\)
\(\,\,\,\,\,\,\approx16.7\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Total outcomes: \(6\)
Favorable outcomes: \(1\)
\(\,\,\,\,\,\,P(4)=\frac{1}{6}\)
\(\,\,\,\,\,\,\approx16.7\%\)
\(\textbf{15)}\) You roll a fair six-sided die one time. What is the probability of rolling an even number?
The answer is \(\frac{1}{2}=50\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Even numbers: 2, 4, 6.
Favorable outcomes: \(3\)
\(\,\,\,\,\,\,P(\text{even})=\frac{3}{6}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Even numbers: 2, 4, 6.
Favorable outcomes: \(3\)
\(\,\,\,\,\,\,P(\text{even})=\frac{3}{6}\)
\(\,\,\,\,\,\,=\frac{1}{2}=50\%\)
\(\textbf{16)}\) You roll a fair six-sided die one time. What is the probability of rolling a number greater than 4?
The answer is \(\frac{1}{3}\approx33.3\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Numbers greater than 4: 5, 6.
Favorable outcomes: \(2\)
\(\,\,\,\,\,\,P(\text{greater than }4)=\frac{2}{6}\)
\(\,\,\,\,\,\,=\frac{1}{3}\approx33.3\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Numbers greater than 4: 5, 6.
Favorable outcomes: \(2\)
\(\,\,\,\,\,\,P(\text{greater than }4)=\frac{2}{6}\)
\(\,\,\,\,\,\,=\frac{1}{3}\approx33.3\%\)
\(\textbf{17)}\) You roll a fair six-sided die one time. What is the probability of rolling a number less than 5?
The answer is \(\frac{2}{3}\approx66.7\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Numbers less than 5: 1, 2, 3, 4.
Favorable outcomes: \(4\)
\(\,\,\,\,\,\,P(\text{less than }5)=\frac{4}{6}\)
\(\,\,\,\,\,\,=\frac{2}{3}\approx66.7\%\)
Possible outcomes: 1, 2, 3, 4, 5, 6.
Numbers less than 5: 1, 2, 3, 4.
Favorable outcomes: \(4\)
\(\,\,\,\,\,\,P(\text{less than }5)=\frac{4}{6}\)
\(\,\,\,\,\,\,=\frac{2}{3}\approx66.7\%\)
\(\textbf{18)}\) A bag contains 8 red marbles, 4 blue marbles, and 3 green marbles. You select 1 marble. What is the probability of selecting a blue or green marble?
The answer is \(\frac{7}{15}\approx46.7\%\)
Total marbles: \(8+4+3=15\)
Blue or green marbles: \(4+3=7\)
\(\,\,\,\,\,\,P(\text{blue or green})=\frac{7}{15}\)
\(\,\,\,\,\,\,\approx46.7\%\)
Total marbles: \(8+4+3=15\)
Blue or green marbles: \(4+3=7\)
\(\,\,\,\,\,\,P(\text{blue or green})=\frac{7}{15}\)
\(\,\,\,\,\,\,\approx46.7\%\)
\(\textbf{19)}\) A bag contains 8 red marbles, 4 blue marbles, and 3 green marbles. You select 1 marble. What is the probability of NOT selecting a red marble?
The answer is \(\frac{7}{15}\approx46.7\%\)
Total marbles: \(8+4+3=15\)
Marbles that are not red: \(4+3=7\)
\(\,\,\,\,\,\,P(\text{not red})=\frac{7}{15}\)
\(\,\,\,\,\,\,\approx46.7\%\)
Total marbles: \(8+4+3=15\)
Marbles that are not red: \(4+3=7\)
\(\,\,\,\,\,\,P(\text{not red})=\frac{7}{15}\)
\(\,\,\,\,\,\,\approx46.7\%\)
\(\textbf{20)}\) A bag contains 6 red marbles, 9 blue marbles, and 5 yellow marbles. You select 1 marble. What is the probability of selecting a red or yellow marble?
The answer is \(\frac{11}{20}=55\%\)
Total marbles: \(6+9+5=20\)
Red or yellow marbles: \(6+5=11\)
\(\,\,\,\,\,\,P(\text{red or yellow})=\frac{11}{20}\)
\(\,\,\,\,\,\,=0.55=55\%\)
Total marbles: \(6+9+5=20\)
Red or yellow marbles: \(6+5=11\)
\(\,\,\,\,\,\,P(\text{red or yellow})=\frac{11}{20}\)
\(\,\,\,\,\,\,=0.55=55\%\)
True or False
\(\textbf{21)}\) In probability, the sample space is the set of all possible outcomes of an experiment.
The statement is True.
The sample space includes every possible outcome of an experiment.
For example, when rolling a six-sided die:
\(\,\,\,\,\,\,S=\{1,2,3,4,5,6\}\)
Therefore, the statement is True.
The sample space includes every possible outcome of an experiment.
For example, when rolling a six-sided die:
\(\,\,\,\,\,\,S=\{1,2,3,4,5,6\}\)
Therefore, the statement is True.
\(\textbf{22)}\) The probability of an event always lies between 0 and 1, inclusive.
The statement is True.
The probability of an impossible event is 0.
The probability of a certain event is 1.
Every probability is between these values.
\(\,\,\,\,\,\,0\leq P(A)\leq1\)
Therefore, the statement is True.
The probability of an impossible event is 0.
The probability of a certain event is 1.
Every probability is between these values.
\(\,\,\,\,\,\,0\leq P(A)\leq1\)
Therefore, the statement is True.
See Related Pages\(\)
\(\bullet\text{ Intro to Probability (Multiple Events)}\)
\(\,\,\,\,\,\,\,\,\text{Probability}=\frac{\text{successful events}}{\text{total events}}\)
\(\bullet\text{ Probability with Coin Tosses}\)
\(\,\,\,\,\,\,\,\,\text{Prob(3 heads)}=\frac{1}{8}\)
\(\bullet\text{ Probability with Marbles }\)
\(\,\,\,\,\,\,\,\,\text{Prob(3 red)}=\frac{7}{20}…\)
\(\bullet\text{ Probability with Dice}\)
\(\,\,\,\,\,\,\,\,\text{Prob(Two 6’s)}=\frac{1}{36}…\)
\(\bullet\text{ Probability with Round Tables}\)
\(\,\,\,\,\,\,\,\,(n-1)!…\)
\(\bullet\text{ Probability with Poker Hands}\)
\(\,\,\,\,\,\,\,\,\text{P(Full House)}=…\)