Calculating Probability for Equally Likely Outcomes
Calculating Probability for Equally Likely Outcomes is a Grade 7 math skill in Reveal Math Accelerated, Unit 10: Probability, where students use the theoretical probability formula P(event) = (number of favorable outcomes) / (total number of outcomes) to compute the likelihood of simple events in sample spaces with equally likely outcomes such as coins, dice, and spinners.
Key Concepts
Property When all possible outcomes have the same chance of occurring, the theoretical probability of an event is defined as: $$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$$.
Examples Rolling a die: On a standard 6 sided die, the probability of rolling an even number (2, 4, or 6) is $P(\text{even}) = \frac{3}{6} = \frac{1}{2}$. Spinning a spinner: For a spinner divided into 8 equal sections where 3 are red and 5 are blue, the probability of landing on red is $P(\text{red}) = \frac{3}{8}$. Random selection: If a bag contains 4 green marbles and 6 yellow marbles, the probability of drawing a green marble is $P(\text{green}) = \frac{4}{10} = \frac{2}{5}$ or $40\%$.
Explanation When every possible outcome in a scenario has the exact same chance of occurring, they are known as equally likely outcomes. To calculate the probability of a specific event, you simply count the number of outcomes that match your event (the favorable outcomes) and divide it by the total number of possible outcomes. This mathematical ratio can then be written as a fraction, a decimal, or a percentage to represent the likelihood of the event happening.
Common Questions
What is the formula for theoretical probability?
P(event) = number of favorable outcomes / total number of equally likely outcomes. For example, rolling a 3 on a standard die has probability 1/6 because there is 1 favorable outcome out of 6 equally likely outcomes.
What does equally likely mean in probability?
Equally likely outcomes each have the same chance of occurring. A fair coin has two equally likely outcomes (heads or tails), and a fair six-sided die has six equally likely outcomes.
How do you list the sample space for a probability problem?
The sample space is the set of all possible outcomes. For flipping two coins, the sample space is HH, HT, TH, TT. Listing all outcomes allows you to count favorable ones accurately.
What is Reveal Math Accelerated Unit 10 about?
Unit 10 covers Probability, including theoretical and experimental probability, sample spaces, simple and compound events, simulations, and making predictions based on probability.