7th Grade - Probability

Overview

If you are rolling a die and want to see your chances of getting a 6, probability can help!

Probability

• A probability is the likelihood of a favorable or specific outcome happening.
• A probability of an event or Outcome always ranges from 0 to 1. The closer it is to 1, the more likely that event will occur.
• Here are a few terms to keep in mind:

• • Sample Space or Total Outcomes: All possible results of an experiment are outcomes. If you are rolling a die, the total outcomes are 6. The sample space, in this case, is 6.
  • Favorable Outcome (s): If you are looking for an even number, the total favorable outcomes are 3.
  • Event: An event is a set of some favorable or all outcomes.

Categories of Probability

There are two categories of probability.

• Theoretical Probability

Theoretical or actual probability where all outcomes are equally likely is:

P(event) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{favorable} \mathrm{outcomes}}{\mathrm{Total} \mathrm{outcomes}}$

• Experimental Probability

Experimental probability is based on data collected from repeated trials or surveys.

P(event) = $\frac{\mathrm{Number} \mathrm{of} \mathrm{favorable} \mathrm{outcomes} \mathrm{based} \mathrm{on} \mathrm{trial} \mathrm{or} \mathrm{survey}}{\mathrm{Total} \mathrm{outcomes}}$

Solved Examples

1. What is the probability of getting 6 when you roll a die?

Total outcomes: 6

Favorable outcome(s): 1

P(Getting 6) = $\frac{1}{6}$

2. You randomly pick a card from a deck of cards. What is the probability that it is of spade suite?

Total outcomes: 52 (52 cards in a deck)

Favorable outcome(s): 13 (13 spade cards)

P(Spades) = $\frac{13}{52} \mathrm{which} \mathrm{is} \frac{1}{4}$

Cheat Sheet

• Probabilities are usually expressed in $\frac{a}{b}$ form.
• A probability of 0 means an event can't occur.
• A probability of 1 means the event is sure to occur.
• Even though the probability is usually expressed as a fraction, it can be expressed as a decimal or percent.