Basic Probability Concepts

Why This Matters for Nursing: Probability helps you understand risk factors, test accuracy, and treatment outcomes. "There's a 20% chance of side effects" or "The test has a 95% accuracy rate" — understanding probability helps you communicate with patients and make informed decisions.

What You Need to Know

Probability measures how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%).

🧠 Memory Trick

Probability = Favorable ÷ Total

P(event) = (Number of ways it can happen) ÷ (Total number of possible outcomes)

"Part over Whole" — just like fractions and percents!

Example: Probability of rolling a 3 on a die = 1/6 (one 3 out of six sides)

Basic Probability Formula

P(Event) = Number of favorable outcomes / Total number of possible outcomes

Example: Drawing a Card

What's the probability of drawing a heart from a standard deck? - Favorable: 13 hearts - Total: 52 cards - P(heart) = 13/52 = 1/4 = 0.25 = 25%

Probability Rules

Complement Rule

The probability something DOESN'T happen = 1 - P(it happens)

P(not A) = 1 - P(A)

Example: If P(rain) = 30%, then P(no rain) = 70%

Addition Rule (OR)

For mutually exclusive events (can't happen at same time): P(A or B) = P(A) + P(B)

Example: P(rolling 1 OR 2) = 1/6 + 1/6 = 2/6 = 1/3

Multiplication Rule (AND)

For independent events (one doesn't affect the other): P(A and B) = P(A) × P(B)

Example: P(heads AND heads) = 1/2 × 1/2 = 1/4

✏️ Worked Examples

Example 1: Simple Probability

Problem: A bag has 3 red, 5 blue, and 2 green marbles. What's the probability of drawing a blue marble?

Step 1 — Count the favorable outcomes. We want blue marbles. There are 5 blue marbles.

Step 2 — Count the total possible outcomes. Total marbles = 3 + 5 + 2 = 10.

Step 3 — Set up the fraction. P(blue) = favorable ÷ total = 5/10.

Step 4 — Simplify. 5/10 = 1/2 = 0.5 = 50%.

Answer: 50% chance of drawing a blue marble