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If you flip three fair coins, what is the probability that you'll get at least two heads?

If you flip three fair coins, what is the probability that you'll get at least two heads?

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Full solution

Q. If you flip three fair coins, what is the probability that you'll get at least two heads?
  1. Count Coin Outcomes: Count the total number of outcomes for flipping one coin.\newlineOutcomes for one coin: Heads (H), Tails (T)\newlineNumber of outcomes for one coin: 22
  2. Calculate Total Outcomes: Calculate the total number of outcomes for flipping three coins.\newlineTotal outcomes for three coins = 2×2×2=82 \times 2 \times 2 = 8
  3. List Possible Outcomes: List all possible outcomes for flipping three coins.\newlineHHH,HHT,HTH,HTT,THH,THT,TTH,TTTHHH, HHT, HTH, HTT, THH, THT, TTH, TTT
  4. Count Favorable Outcomes: Count the favorable outcomes where we get at least two heads.\newlineFavorable outcomes: HHHHHH, HHTHHT, HTHHTH, THHTHH\newlineNumber of favorable outcomes: 44
  5. Calculate Probability: Calculate the probability of getting at least two heads.\newlineProbability = Number of favorable outcomes / Total number of outcomes\newlineProbability = 48\frac{4}{8}\newlineProbability = 12\frac{1}{2}

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