Probability can be written as a fraction that describes the likelihood of a particular outcome.
Probability Fraction
\(\mathsf{ \text{P(event)} = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} }\)
Question
What is the probability of a coin landing on heads?
Work through the problems presented in the tabs below to calculate the probabilities of these different events.
Songs
Pop Quiz
Keep Rolling
Pick a Card
Your MP3 player has 100 songs and plays them randomly. The songs are divided into five different categories, which means there are 20 songs per category. What is the probability of hearing a song from the jazz category?
Solve this problem by using the steps in the table below.
| What is the number of possible outcomes? | Since you have 100 songs, you have 100 possible outcomes. |
| What is the number of desired outcomes? | Each category has 20 songs. So you have 20 desired outcomes in the jazz category. |
| How do you calculate the probability of an event? | \(\mathsf{ \text{P(event)} = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} }\) |
| What is the probability of randomly hearing a jazz song? | \(\mathsf{ \text{P(jazz)} = \frac{20}{100} = \frac{1}{5} = 20\% }\) Therefore, you have a 20% chance of randomly hearing a jazz song. |
Your teacher will randomly give a pop quiz one day next week. What is the probability of having the quiz on Thursday?
| What is the number of possible outcomes? | Since there are five days in the school week, you have five possible outcomes. |
| What is the number of desired outcomes? | The desired outcome is Thursday. Therefore, you have one desired outcome. |
| How do you calculate the probability of an event? | \(\mathsf{ \text{P(event)} = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} }\) |
| What is the probability of randomly having a pop quiz on Thursday? | \(\mathsf{ \text{P(quiz)} = \frac{1}{5} = 20\% }\) Therefore, you have a 20% chance of having a quiz on Thursday. Furthermore, if you repeat this problem for any other weekday, you'll see that you have a 20% chance of having the quiz on any school day next week. |
You're playing a game with two friends by rolling a single die. The person who rolls the lowest number wins each round. During this round, your friends rolled 3 and 4. What is the probability of you winning this round?
| What is the sample space of a single die? | The sample space is the set of all possible outcomes. Therefore, the sample space for a single die is [1, 2, 3, 4, 5, 6] |
| What is the number of possible outcomes? | Because a die has six numbers, there are six possible outcomes. |
| What is the number of desired outcomes? | You must roll either a 1 or 2 to win the round. Therefore, you have two desired outcomes. |
| How do you calculate the probability of an event? | \(\mathsf{ \text{P(event)} = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} }\) |
| What is the probability of winning this round? | \(\mathsf{ \text{P(winning)} = \frac{2}{6} = \frac{1}{3} = 33\% }\) Therefore, you have a 33% chance of winning this round of the game. |
You're randomly choosing cards from a standard deck of 52 cards. The deck has four suits with 13 cards in each suit. What is the probability that you will choose a queen?
| What is the number of possible outcomes? | The deck has 52 cards and, therefore, 52 possible outcomes. |
| What is the number of desired outcomes? | A standard deck has four queens (one in each suit). Hence, you have four desired outcomes. |
| How do you calculate the probability of an event? | \(\mathsf{ \text{P(event)} = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} }\) |
| What is the probability of randomly choosing a queen? | \(\mathsf{ \text{P(queen)} = \frac{4}{52} = \frac{1}{13} = 8\% }\) You have an 8% chance of randomly choosing a queen from the deck. |
