Calculating Probability
Calculating probability for equally likely outcomes uses the formula P(event) = number of favorable outcomes ÷ total number of possible outcomes. In Grade 6 Saxon Math Course 1, students apply this to standard experiments: rolling a die, drawing from a set, spinning a spinner. The probability of rolling a 3 on a standard die is 1/6; the probability of drawing a red card from a standard deck is 26/52 = 1/2. Probability values range from 0 (impossible) to 1 (certain).
Key Concepts
Property If all outcomes of an experiment have the same probability, then the probability of an event is: $$ \frac{\text{number of outcomes in the event}}{\text{number of possible outcomes}} $$.
Examples Probability of rolling an odd number on a die: $P(\text{odd}) = \frac{\text{outcomes } \{1, 3, 5\}}{6 \text{ total outcomes}} = \frac{3}{6} = \frac{1}{2}$ Probability of drawing a King from a 52 card deck: $P(\text{King}) = \frac{4}{52} = \frac{1}{13}$ From a bag with 5 red and 7 other marbles, the probability of drawing red is: $P(\text{red}) = \frac{5}{12}$.
Explanation When every outcome has a fair shot, calculating probability is just a simple fraction! Count how many ways you can 'win' (the outcomes you want) and put that number on top. Then, count all the things that could possibly happen (the whole sample space) and put that on the bottom. Voilà, you’ve got the probability of your event.
Common Questions
What is the formula for calculating probability?
P(event) = number of favorable outcomes ÷ total number of possible outcomes.
What is the probability of rolling a 3 on a standard six-sided die?
1 favorable outcome ÷ 6 total outcomes = 1/6.
A bag has 4 red, 3 blue, and 5 green marbles. What is P(blue)?
3 favorable ÷ 12 total = 3/12 = 1/4.
What probability value means an event is certain?
P = 1 (or 100%). All outcomes are favorable.
What probability value means an event is impossible?
P = 0 (or 0%). No outcomes are favorable.