1. What is Conditional Probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. In coin flipping, it helps us understand how the probability of one outcome changes based on information about another outcome.

2. How Does the Calculator Work?

The calculator uses the conditional probability formula:

Where:

• \( P(A|B) \) — Probability of A given B
• \( P(A \text{ and } B) \) — Probability of both A and B occurring
• \( P(B) \) — Probability of event B

3. Coin Flip Examples

Example 1: What's the probability of getting two heads (A) given that at least one flip is heads (B) when flipping two coins?
P(A and B) = 1/4 (only HH satisfies both), P(B) = 3/4 (HH, HT, TH), so P(A|B) = (1/4)/(3/4) = 1/3 ≈ 0.3333

Example 2: Probability of second flip being heads (A) given first flip was tails (B)?
P(A and B) = 1/4 (TH), P(B) = 1/2 (TH, TT), so P(A|B) = (1/4)/(1/2) = 1/2 = 0.5

4. Using the Calculator

Tips: Enter probabilities as values between 0 and 1. For coin flips, these are typically fractions converted to decimals (e.g., 0.5 for 1/2).

5. Frequently Asked Questions (FAQ)

Q1: Why use conditional probability for coin flips?
A: It helps analyze dependent events where the outcome of one flip affects the probability of another.

Q2: What's the difference between P(A|B) and P(B|A)?
A: They measure different relationships - P(A|B) is probability of A given B occurred, while P(B|A) is the reverse.

Q3: How is this different from independent events?
A: For independent events, P(A|B) = P(A). For dependent events (like sequential coin flips with conditions), they differ.

Q4: Can this calculator handle more than two events?
A: This version handles two events. More complex scenarios would need expanded calculations.

Q5: What if P(B) is zero?
A: Conditional probability is undefined when the given event has zero probability (division by zero).