1. What is Coin Flip Probability?

The coin flip probability calculates the chance of getting exactly k successes (e.g., heads) in n independent Bernoulli trials (flips) with probability p=0.5 for each trial. This models a fair coin with equal probability for heads and tails.

2. How Does the Calculator Work?

The calculator uses the binomial probability formula:

Where:

• \( n \) — Number of coin flips
• \( k \) — Number of desired successes (e.g., heads)
• \( \binom{n}{k} \) — Binomial coefficient ("n choose k")

Explanation: The formula accounts for all possible sequences that give exactly k successes in n flips, with each sequence having probability (1/2)^n.

3. Importance of Probability Calculation

Details: Understanding coin flip probabilities is fundamental in probability theory and has applications in statistics, game theory, and decision making.

4. Using the Calculator

Tips: Enter the total number of flips and desired number of heads (or tails). The number of successes must be less than or equal to the number of flips.

5. Frequently Asked Questions (FAQ)

Q1: What if I want at least k successes?
A: You would need to sum the probabilities for k, k+1, ..., n successes.

Q2: Does this work for unfair coins?
A: No, this calculator assumes a fair coin (p=0.5). For unfair coins, use \( p^k(1-p)^{n-k} \binom{n}{k} \).

Q3: What's the probability of exactly 5 heads in 10 flips?
A: About 24.61% (0.24609375 exactly).

Q4: How does this relate to the normal distribution?
A: For large n, the binomial distribution approximates a normal distribution (Central Limit Theorem).

Q5: What is the binomial coefficient?
A: It represents the number of ways to choose k successes from n trials, calculated as \( \frac{n!}{k!(n-k)!} \).