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Apply Scientific
Probability

Use probability and statistics to predict outcomes, interpret data, and reason about uncertainty in scientific contexts.

GED Science

What Is Probability?

Probability measures how likely an event is to happen. It is always a number between 0 (impossible) and 1 (certain), and can be written as a fraction, decimal, or percent.

The Probability Scale

0 0.5 1 Impossible Even chance Certain Unlikely Likely

Why It Matters in Science

Genetics
Predict the chance of inheriting a trait using Punnett squares.
Medicine
Estimate the effectiveness or risk of a treatment.
Weather
Forecast the likelihood of rain or storms.

Theoretical Probability

Theoretical probability is based on reasoning about equally likely outcomes — what *should* happen in an ideal situation.

Rolling a fair six-sided die 1 2 3 4 5 6
\( P(\text{rolling a } 3) = \frac{1}{6} \)

Experimental Probability

Experimental probability is based on actual data from trials or observations — what really happened.

Theoretical vs. Experimental

Theoretical Experimental
Based onReasoning & logicReal data & trials
When usedOutcomes equally likelyObserved results
Example\( P = \frac{1}{6} \) for a die17 of 100 actual rolls

How to Apply Probability

1
Identify the event. What specific outcome are you asking about?
2
Count favorable outcomes. How many outcomes match the event?
3
Count total outcomes. How many outcomes are possible in all?
4
Divide and convert. Compute \( \frac{\text{favorable}}{\text{total}} \), then express as a decimal or percent.

Example 1: Marbles

A bag contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?

4 red 3 blue 5 green

Example 2: Genetics

Cross two parents who are both heterozygous (Bb) for brown eyes. What is the probability their child has blue eyes (genotype bb)?

B b B b BB Bb Bb bb
\( P(\text{genotype is } bb) = \frac{1}{4} \)

Example 3: Two Events

For independent events, multiply their probabilities. A coin is flipped and a die is rolled. What is the probability of getting heads AND a 4?

Common Mistakes

✕ Wrong total
Forgetting to add ALL outcomes when finding the denominator.
✕ Adding instead of multiplying
For "A and B" independent events, multiply probabilities — don't add them.
✕ Probability over 1
A valid probability is never greater than 1 (or 100%). Recheck your math.

Probability Summary

Situation Rule
Single event\( \frac{\text{favorable}}{\text{total}} \)
"A and B" (independent)\( P(A) \times P(B) \)
"A or B" (mutually exclusive)\( P(A) + P(B) \)
Complement (NOT A)\( 1 - P(A) \)

Let's Practice

Question 1 of 5

A spinner has 8 equal sections numbered 1 through 8. What is the probability of landing on an even number?

Question 2 of 5

In 200 plant seeds, 150 germinated. What is the experimental probability that a seed germinates?

Question 3 of 5

Two heterozygous parents (Tt × Tt) are crossed. What is the probability of an offspring being homozygous recessive (tt)?

Question 4 of 5

A coin is flipped twice. What is the probability of getting heads both times (independent events)?

Question 5 of 5

If the probability of rain tomorrow is 0.30, what is the probability that it does NOT rain?

You've Got the Tools

You can now apply probability in scientific contexts — from genetics to weather forecasting.

Basic formula
\( \frac{\text{favorable}}{\text{total}} \)
And rule
\( P(A) \times P(B) \)
Complement
\( 1 - P(A) \)