Understanding Coin Flip Probability
Coin flip probability is a fundamental concept in statistics and probability theory. A single flip of a fair coin has two equally likely outcomes: heads or tails, each with a probability of 0.5 or 50%.
When you flip a coin multiple times, you can calculate the probability of getting a specific number of heads (or tails) using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
n = number of flips
k = desired number of heads
p = probability of heads on a single flip
C(n, k) = binomial coefficient ("n choose k")
Our calculator does this math for you instantly, whether you want the probability of an exact number of heads, at least that many, or at most that many.
Related Tools & Guides
Explore more random generators and probability tools:
- Random Number Generator – Generate numbers in any range.
- Virtual Coin Flip – Flip a coin online.
- Probability of Dice Rolls – Calculate dice roll odds.
- Decision Wheel – Let chance make a choice for you.
Privacy Note: All calculations are performed locally in your browser. No data is sent to our servers, ensuring your privacy.
Frequently Asked Questions
How is the probability of multiple coin flips calculated?
The probability of a specific sequence of coin flips (like HTH) is calculated by multiplying the probability of each individual flip. For a fair coin, each flip has a 0.5 (50%) chance. So, the probability of HTH is 0.5 * 0.5 * 0.5 = 0.125 or 12.5%.
What is the probability of getting exactly 3 heads in 5 flips?
The probability of getting exactly k heads in n flips is given by the binomial probability formula. For exactly 3 heads in 5 flips of a fair coin, the probability is 31.25%. You can use the calculator above to find this by setting the number of flips to 5 and the desired heads to 3.
Does a previous coin flip affect the next one?
No. For a fair coin, each flip is an independent event. The outcome of one flip does not influence the next. This is known as the Gambler's Fallacy—the mistaken belief that past events affect future independent events.
Can I calculate the probability for an unfair (biased) coin?
Yes, the calculator allows you to adjust the probability of heads. Simply change the 'Probability of Heads' field from the default 0.5 (50%) to your desired value, such as 0.6 for a coin biased towards heads.