Combination Calculator Calculate Combinations. Show Work.

Answers Binomial Probability Calculator

What is the probability of exactly 4 heads in 6 coin flips?

This is a binomial probability question because each coin flip is an independent trial with the same success probability, and the question asks for an exact success count.

Probability result

23.4375%

Exact fraction: 15/64

Decimal: 0.234375

The probability of exactly 4 successes is 23.4375%.

For a fair coin, the chance of heads on each flip is 1/2. The binomial model counts how many 6-flip sequences contain exactly 4 heads and 2 tails.

Worked steps

Show your work

  1. Inputs: trials = 6, target successes = 4, p = 0.5, event = exactly.
  2. Formula: P(X = k) = C(n, k)p^k(1-p)^(n-k).
  3. Substitute: use C(6, k) with p = 1/2 and 1-p = 1/2.
  4. Steps: evaluate the binomial term for X = 4 and combine them.
  5. Result: The probability of exactly 4 successes is 23.4375%.

Interactive tool

Verify the same values in the calculator

For a fair coin, the chance of heads on each flip is 1/2. The binomial model counts how many 6-flip sequences contain exactly 4 heads and 2 tails.

Formula

Probability model

P(E) = favorable outcomes / total outcomes

Use the model that matches the setup wording.

Probability

0%

Enter values to calculate.

Exact fraction --
Decimal --

What your result means

The explanation updates with the current inputs.

Calculation work