Probability expresses how likely an event is to occur as a number from 0 to 1.
Probability Formula
P(A) = (number of ways A occurs) ÷ (number of all possible outcomes)
Range of probability: 0 ≦ P(A) ≦ 1. The probability of an event that must occur is 1, and the probability of an event that can never occur is 0.
Example ①
When a die with faces numbered 1〜6 is rolled once, find the probability of rolling an even number.
Solution: There are 6 possible outcomes. The even numbers (2,4,6) give 3 outcomes. P = 3/6 = 1/2
When a die with faces numbered 1〜6 is rolled once, find the probability of rolling an even number.
Solution: There are 6 possible outcomes. The even numbers (2,4,6) give 3 outcomes. P = 3/6 = 1/2
Key Points
- The outcomes must be “equally likely”
- Always answer with a fraction in lowest terms or a decimal
- 0 ≦ P(A) ≦ 1
Practice Problems
- When a die is rolled once, find the probability of rolling a multiple of 3.
- When one card is drawn from cards numbered with the integers 1〜10, find the probability of drawing a prime number.
Answers and Explanations
- Answer: 1/3. There are 2 multiples of 3: 3 and 6. 2/6=1/3.
- Answer: 2/5. There are 4 prime numbers: 2,3,5,7. 4/10=2/5.