How to find theoretical probability

Answer

The Basic Formula for Calculating Theoretical Probability

$\text{Theoretical Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Steps to Find Theoretical Probability

1. Identify all possible outcomes - List every outcome that could occur in the situation
2. Count the total possible outcomes - This becomes your denominator
3. Identify favorable outcomes - Determine which outcomes match the event you're interested in
4. Count the favorable outcomes - This becomes your numerator
5. Calculate the probability - Divide favorable by total, expressing as a fraction, decimal, or percentage

Examples

Rolling a die and getting a 4:

• Total possible outcomes: 6 (the numbers 1, 2, 3, 4, 5, 6)
• Favorable outcomes: 1 (only the number 4)
• Theoretical probability: $\frac{1}{6}\approx 0.167\text{ or }16.7\mathrm{\%}$

Flipping a coin and getting heads:

• Total possible outcomes: 2 (heads or tails)
• Favorable outcomes: 1 (heads)
• Theoretical probability: $\frac{1}{2}=0.5\text{ or }50\mathrm{\%}$

Drawing a heart from a standard deck of cards:

• Total possible outcomes: 52 cards
• Favorable outcomes: 13 (all hearts)
• Theoretical probability: \(\frac{13}{52} = \frac{1}{4} = 0.25 \text{ or } 25\%\)

Key Assumptions

Theoretical probability assumes that all outcomes are equally likely to occur. This works for fair dice, coins, and shuffled cards, but wouldn't apply to situations where outcomes have different likelihoods.

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