How to Solve Theoretical Probability?
How to find theoretical probability?
Step 1: Identify the number of favorable outcomes. Since there are \(20\) lottery tickets, \(20\) will be the desired number of results.
Solve Theoretical Probability: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- List outcomesName the possible results or count them carefully.
- Choose the ruleUse addition, multiplication, or conditional probability based on the wording.
- Check the rangeA probability must be between 0 and 1.
Worked examples
Simple probability
- Even outcomes are 2, 4, and 6.
- There are 3 favorable outcomes out of 6.
- Reduce the fraction.
Independent events
- P(heads) = 1/2 for each flip.
- The flips are independent.
- Multiply 1/2 by 1/2.
Try one before moving on
Solve Theoretical Probability: pop-up practice
Step 2: Determine the total possible outcomes. Since a total of \(600\) tickets were sold in this way, \(600\) will be the total number of possible results.
Step 3: Divide the value from step \(1\) by step \(2\) to calculate the theoretical probability. Therefore, \(\frac{20}{600}=0.03\). This indicates that the probability of a person winning a lottery prize is \(0.03\).
Theoretical Probability – Example 1:
Find the probability of getting \(2\) on a fair die.
Solution:
The possible outcomes of rolling a die are \(1, 2, 3, 4, 5, 6\), so the total number of outcomes \(=6\). As we want to calculate the probability of getting only \(2\), therefore, the number of desired outcomes \(= 1\).
\(p\left(2\right)=\frac{1}{6}=0.16\)
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