TATITIC CALCULATOR
Coin Flipper
A precise tool.
What is the Coin Flipper & How does it work?
A coin flip is a classic example of a Bernoulli trial, where each flip results in either heads (success) or tails (failure) with a fixed probability. When many independent flips are performed, the number of heads follows a binomial distribution.
The probability of observing exactly k heads in n flips is given by the binomial formula.
P(X = k) = \binom{n}{k} p^{k} (1-p)^{n-k}
n = total flips, k = heads count, p = probability of heads
From this distribution you can also derive the expected number of heads E[X] = n·p and the variance Var(X) = n·p·(1-p), which are useful for assessing fairness and risk.
Parameters
Result
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Frequently Asked Questions
How do I calculate the probability of getting exactly 3 heads in 5 coin flips?
Use the binomial formula: P(X = k) = binom{n}{k} p^{k} (1-p)^{n-k}, where n=5, k=3, and p=0.5 for a fair coin.
What is the expected number of heads in 10 coin flips?
The expected number of heads is np, so for 10 flips with p=0.5, it's 10 * 0.5 = 5 heads.
Can this calculator handle biased coins?
Yes, you can input a different probability for heads (p) to account for a biased coin.
How does the binomial distribution apply to real-world scenarios?
It's used in various fields like quality control, genetics, and polling to model situations with two possible outcomes.
What is the difference between a Bernoulli trial and a binomial distribution?
A Bernoulli trial is one coin flip with two outcomes. A binomial distribution models multiple independent Bernoulli trials.
How do I interpret the results from this calculator?
The result gives you the probability of getting exactly k heads in n flips, helping you understand the likelihood of different outcomes.
Can this calculator be used for more than just coin flips?
Yes, it can be adapted for other binary outcome scenarios like success/failure experiments.
Results are for informational purposes only and do not constitute professional advice.