Here is a summary of the key points in Chapter 9 on Probability from 7th grade Course 2:
- Probability is the chance that an event will occur. It is expressed as a fraction from 0 to 1, or as a percentage from 0% to 100%.
- An event is certain to occur if it has a probability of 1 or 100%. An impossible event has a probability of 0.
- The probability of an event is found by counting the number of favorable outcomes and dividing by the total number of possible outcomes.
P(event) = number of favorable outcomes/total number of possible outcomes
- When outcomes are equally likely, the probability is found by dividing the number of favorable outcomes by the total number of possible outcomes.
- When outcomes are not equally likely, probabilities can be determined using game models, simulation, or experimental data.
- Events can be independent, mutually exclusive, or dependent. Independent events do not affect each other. Mutually exclusive events cannot both occur. Dependent events affect each other.
- The probability of two independent events both occurring is found by multiplying their individual probabilities.
P(A and B) = P(A) × P(B)
- The probability of at least one of two independent events occurring is found by adding their individual probabilities.
P(A or B) = P(A) + P(B)
- The probability that an event does NOT occur is 1 minus the probability that it does occur.
P(not A) = 1 - P(A)
Hope this summary helps! Let me know if you have any other questions.