Mathematics Topic
Probability
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Study focus - 3 things
- Probability measures how likely an event is
- The probability of an event ranges from 0 to 1
- For equally likely outcomes, probability = favourable outcomes / total outcomes
Section 1Probability scale
Probability is a number from 0 to 1. A probability of 0 means impossible, 1 means certain, and 1/2 means equally likely to happen or not happen.
Section 2Equally likely outcomes
When outcomes are equally likely, use probability = favourable outcomes divided by total possible outcomes. For example, the probability of rolling a 4 on a fair die is 1/6.
Section 3Complements
The complement is the event not happening. P(not A) = 1 - P(A). If the chance of rain is 0.3, the chance of no rain is 0.7.
Section 4Experimental probability
Experimental probability uses results from trials: number of successful trials divided by total trials. It may not exactly match theoretical probability, especially with few trials.
Section 5Writing answers
Probability can be written as a fraction, decimal, or percentage. Keep answers simplified when using fractions, and check that the answer is not greater than 1.
Examples
A bag has 3 red balls and 5 blue balls. Find the probability of picking a red ball.
There are 3 favourable red balls and 8 balls in total, so P(red) = 3/8.
A fair die is rolled. Find the probability of rolling an even number.
The even outcomes are 2, 4, and 6. There are 3 favourable outcomes out of 6, so P(even) = 3/6 = 1/2.
Now let's water it
Session runs notes to flashcards to quiz back-to-back.