📊 Advanced Probability Calculator

📚 Quick Examples (click to try):

Number of favorable outcomes

Total possible outcomes

🎰 Expected Outcomes

Expected Successes

Expected Failures

Std Deviation

95% Range

📝 What This Means

Probability per trial: 50%

Number of trials: 100

Interpretation: —

📊 Expected Distribution

📈 Bell Curve (Normal Approximation)

💡 Understanding the Results

Expected Value: The average number of successes you'd get if you repeated this experiment many times.
Standard Deviation: Measures how spread out the results typically are from the expected value.
95% Range: About 95% of the time, your actual results will fall within this range.
Simulation: Click "Simulate" to see what actually happens in one run of the experiment!

📖 How to Use

1 Choose Mode:

Select Single Event, Two Events, or Repeated Trials from the tabs.

2 Enter Values:

Fill in the required fields or click a quick example button.

3 Calculate:

Click "Calculate Probability" to see results.

4 View Results:

See probability as fraction, decimal, and percentage with visual charts.

💡 Example Scenarios

🎲 Single Event

Q: What's the probability of rolling a 4 on a dice?

A: Favorable = 1, Total = 6

Result: 1/6 = 16.67%

🔗 Two Events

Q: P(A)=50%, P(B)=40%, independent. What's P(A AND B)?

A: P(A∩B) = 0.5 × 0.4

Result: 20%

🔄 Repeated Trials

Q: 3 coin flips, what's P(all heads)?

A: P = 0.5³

Result: 12.5%

🎰 Expected Outcomes

Q: Flip coin 100 times, how many heads?

A: Expected = 100 × 0.5

Result: ~50 heads (range: 40-60)

📐 Formula Reference

Single Event:

P = favorable / total

Two Events (Independent):

P(A∩B) = P(A) × P(B)

P(A∪B) = P(A) + P(B) − P(A∩B)

Repeated Trials:

All: Pⁿ

At least 1: 1 − (1−P)ⁿ

Expected Outcomes:

Expected = n × p

Std Dev = √(n × p × (1−p))

95% Range = Expected ± 2σ

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🎯

Single Event

Dice, coins, cards

🔗

Two Events

A and B, A or B

🔄

Repeated Trials

Multiple attempts

🎰

Expected Outcomes

Predict results

📊

Visual Charts

Pie & Bar graphs

❓ Frequently Asked Questions

What is probability? ▼

Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%). A probability of 0 means the event cannot happen, while 1 means it will definitely happen.

What's the difference between independent and dependent events? ▼

Independent events: One event doesn't affect the other (e.g., flipping a coin twice).
Dependent events: One event affects the probability of the other (e.g., drawing cards without replacement).

When should I use "A AND B" vs "A OR B"? ▼

Use A AND B (P(A∩B)) when you want BOTH events to occur simultaneously.
Use A OR B (P(A∪B)) when you want AT LEAST ONE of the events to occur.

How do I calculate "at least once" probability? ▼

The easiest way is to calculate the probability of the event NEVER happening, then subtract from 1:
P(at least once) = 1 − (1 − p)ⁿ
Where p is the single-trial probability and n is the number of trials.

Can probability be greater than 100%? ▼

No! Probability is always between 0% and 100% (or 0 and 1 in decimal form). If you get a result greater than 100%, check your inputs for errors.

🎲 Probability Calculator