Probability
In short: Probability rates the chance of an event on a scale from 0 to 1, where a rating of 0 marks something that cannot occur and a rating of 1 marks something sure to occur.
7th GradeProbability7.SP.C.5
What is Probability?
Whether a spinner stops on red or it rains tomorrow, the chance of the event gets a probability, a fraction, decimal or percent running from 0 up to 1 (0% up to 100%).
When all outcomes are equally likely, \(P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\). Near 0 means unlikely, near \(\frac{1}{2}\) means a toss-up, near 1 means likely. The probabilities of an event and of its opposite always add to 1.
How to spot it
- A problem asks how likely, what are the chances, or what fraction of the time something will happen.
- Items are drawn from a bag, spun on a spinner, rolled with dice or picked from a deck.
- Answers are expected as a fraction, decimal or percent no greater than 1 or 100%.
- Words like impossible, unlikely, equally likely, likely and certain describe an event.
The method
- List every possible outcome and count them to get the total.
- Count the outcomes that match the event you want, the favorable outcomes.
- Write the fraction favorable over total and simplify it.
- Convert to a decimal or percent if asked, and check that the answer lies between 0 and 1.
Probability: solved example
Problem
A jar of glass beads contains 6 amber, 12 teal and 12 violet beads. One bead is pulled out blindly. How likely is a violet one?
Solution
Beads in all: \(6 + 12 + 12 = 30\). Violet beads: 12.
\(P(\text{violet}) = \frac{12}{30} = \frac{2}{5} = 0.4\). The chance is \(\frac{2}{5}\), or 40%.
Try it
Question 1
A spinner has 12 equal sections and 3 are shaded. What is the probability of landing on a shaded section?
Show the answer
\(\frac{3}{12} = \frac{1}{4}\), or 25%.
Question 2
The chance of snow tomorrow is \(\frac{3}{10}\). What is the chance of no snow?
Show the answer
The two chances add to 1, so \(1 – \frac{3}{10} = \frac{7}{10}\).
Probability vs. Experimental Probability
This number can describe an ideal setup before anything is tried, or it can summarize what happened in actual trials. Theoretical values come from counting equally likely outcomes; experimental values come from results recorded in a test. They tend to get closer as the number of trials grows.
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Related words
Whole dictionary: A–Z · 7th Grade · Probability