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What is the probability of at least 1 head in 4 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 a success-count range.

Probability result

93.75%

Exact fraction: 15/16

Decimal: 0.9375

The probability of at least 1 success is 93.75%.

For a fair coin, the chance of heads on each flip is 1/2. At least 1 head means every outcome is satisfactory except the single all-tails sequence.

Worked steps

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  1. Inputs: trials = 4, target successes = 1, p = 0.5, event = at least.
  2. Formula: P(X in range) = sum of C(n, k)p^k(1-p)^(n-k) terms.
  3. Substitute: use C(4, k) with p = 1/2 and 1-p = 1/2.
  4. Steps: evaluate the binomial terms for X >= 1 and combine them.
  5. Result: The probability of at least 1 success is 93.75%.

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For a fair coin, the chance of heads on each flip is 1/2. At least 1 head means every outcome is satisfactory except the single all-tails sequence.

Formula

Probability model

P(E) = favorable outcomes / total outcomes

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