Coin Flip Probability Calculator

This calculator uses the binomial probability formula to compute various probabilities for coin flip experiments:

• Enter the total number of coin flips in your experiment
• Specify the target number of heads you want to calculate probabilities for
• Set the probability of getting heads on a single flip (0.5 for a fair coin)
• The calculator will show you:
  • Exact probability of getting the target number of heads
  • Probability of getting at least that many heads (cumulative probability)
  • Probability of getting at most that many heads (cumulative probability)
  • Number of possible combinations for achieving the target number of heads

Coin flip experiments follow the binomial probability distribution, which has these key characteristics:

• Each flip is independent (the outcome of one flip doesn't affect others)
• There are exactly two possible outcomes for each trial (heads or tails)
• The probability remains constant for each flip (assuming the same coin is used)
• The number of trials (flips) is fixed before the experiment begins

The calculator uses the binomial probability formula:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Where:

• n = total number of flips
• k = target number of heads
• p = probability of heads on a single flip
• C(n,k) = number of ways to choose k items from n items

This calculator is useful for various applications:

• Educational demonstrations of probability concepts
• Statistical analysis of binary outcomes
• Probability theory research and study
• Game theory and decision making
• Risk assessment in binary outcome scenarios