Coin Flip Probability Calculator

It uses the binomial formula. The chance of exactly k heads in n flips is C(n, k) times p to the power k times (1 minus p) to the power (n minus k), where p is the chance of heads on one flip and C(n, k) counts the ways to choose which flips are heads.

About 24.61 percent. There are C(10, 5) = 252 ways to get 5 heads out of 10 flips, and each specific sequence has probability 0.5 to the power 10, which is 1 in 1024. So the chance is 252 divided by 1024.

At least adds up the chances of the target heads count and every higher count, so at least 8 of 10 covers 8, 9, and 10 heads. At most adds the target and every lower count. Exactly counts only the single target number of heads.

Yes. Set the heads probability to any value between 0 and 1. A coin that lands heads 70 percent of the time uses 0.7. The formula weights each sequence by that probability, so the results reflect the bias automatically.

For a fair coin the single most likely outcome is the count nearest half the flips, but its probability is still well under 50 percent because it competes with many nearby counts. As you flip more coins the distribution spreads, so any one exact count becomes less likely even as the average stays at half.