~ 8.3 ~
What are Probabilities?
Learning Targets
I can use the sample space to calculate the probability of an event when all outcomes are equally likely.
I can write out the sample space for a simple chance experiment.
Notes
The probability of an event is a measure of the likelihood that the event will occur. Probabilities are expressed using numbers from 0 to 1.
f the probability is 0, that means the event is impossible. For example, when you flip a coin, the probability that it will turn into a bottle of ketchup is 0. The closer the probability of some event is to 0, the less likely it is.
If the probability is 1, that means the event is certain. For example, when you flip a coin, the probability that it will land somewhere is 1. The closer the probability of some event is to 1, the more likely it is.
If we list all of the possible outcomes for a chance experiment, we get the sample space for that experiment. For example, the sample space for rolling a standard number cube includes six outcomes: 1, 2, 3, 4, 5, and 6. The probability that the number cube will land showing the number 4 is ⅙. In general, if all outcomes in an experiment are equally likely and there are possible outcomes, then the probability of a single outcome is 1/n.
Sometimes we have a set of possible outcomes and we want one of them to be selected at random. That means that we want to select an outcome in a way that each of the outcomes is equally likely. For example, if two people both want to read the same book, we could flip a coin to see who gets to read the book first.
Vocabulary
probability
The probability of an event is a number that tells how likely it is to happen. A probability of 1 means the event will always happen. A probability of 0 means the event will never happen.
For example, the probability of selecting a moon block at random from this bag is ⅘.
random
Outcomes of a chance experiment are random if they are all equally likely to happen.
sample space
The sample space is the list of every possible outcome for a chance experiment.
For example, the sample space for tossing two coins is:
heads-heads
heads-tails
tails-heads
tails-tails
Activities
3.1 Which Game Would You Choose?
Which game would you choose to play? Explain your reasoning.
Game 1: You flip a coin and win if it lands showing heads.
Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.
3.2 What’s Possible?
For each situation, list the sample space and tell how many outcomes there are. Remember…each possible results for a chance experiment is called an outcome
Han rolls a standard number cube once.
Clare spins this spinner once.
Kiran selects a letter at random from the word “MATH.”
Mai selects a letter at random from the alphabet.
Noah picks a card at random from a stack that has cards numbered 5 through 20.
Next, compare the likelihood of these outcomes. Be prepared to explain your reasoning.
Is Clare more likely to have the spinner stop on the red or blue section?
Is Kiran or Mai more likely to get the letter T?
Is Han or Noah more likely to get a number that is greater than 5?
Suppose you have a spinner that is evenly divided showing all the days of the week. You also have a bag of papers that list the months of the year. Are you more likely to spin the current day of the week or pull out the paper with the current month?
Clare's Spinner
Add to Your Notes
In this activity, all of the outcomes are equally likely within each sample space.
Sometimes it is important to have an actual numerical value rather than a sense of likelihood.
To answer how probable something is to happen, we assign a probability.
Probabilities are values between 0 and 1 and can be expressed as a fraction, decimal, or percentage.
Example: Something that has 50% chance of happening, like a coin landing heads up, or the probability is ½ or 0.5.
desired outcomes
total outcomes
Assignment
Check Google Classroom!