What is "if you flip three fair coins?

Flipping three fair coins is a classic probability experiment that demonstrates basic concepts like sample space, probability, and independent events.

• Sample Space: The <a href="https://www.wikiwhat.page/kavramlar/sample%20space">sample space</a> represents all possible outcomes. When flipping three coins, each coin can land as either Heads (H) or Tails (T). Thus, the sample space is: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. There are 2 x 2 x 2 = 8 possible outcomes.

• Probability of Outcomes: Since the coins are fair, each outcome in the <a href="https://www.wikiwhat.page/kavramlar/sample%20space">sample space</a> is equally likely. Therefore, the probability of any single outcome (e.g., HHT) is 1/8.

• Calculating Probabilities of Events: You can calculate the probability of specific events by counting the number of outcomes in the <a href="https://www.wikiwhat.page/kavramlar/sample%20space">sample space</a> that satisfy the event and dividing by the total number of outcomes (8). For example:

  • Probability of getting exactly two heads: There are three outcomes with exactly two heads (HHT, HTH, THH), so the probability is 3/8.
  • Probability of getting at least one head: There are seven outcomes with at least one head (all except TTT), so the probability is 7/8.
  • Probability of getting all tails: There is only one outcome with all tails (TTT), so the probability is 1/8.

• Independent Events: Each coin flip is an <a href="https://www.wikiwhat.page/kavramlar/independent%20events">independent event</a>, meaning the outcome of one flip does not affect the outcome of the other flips. This is crucial for calculating probabilities of combined events.