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Make an organized list to show all possible outcomes when four fair coins are flipped. Each coin lands facing either heads up (H) or tails up (T). What is the probability that at least three coins land facing tails up?

Question

Make an organized list to show all possible outcomes when four fair coins are flipped. Each coin lands facing either heads up (H) or tails up (T). What is the probability that at least three coins land facing tails up?

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Solution

Step 1: List all possible outcomes when four fair coins are flipped.

There are 2^4 = 16 possible outcomes when four fair coins are flipped. These are:

  1. HHHH
  2. HHHT
  3. HHTH
  4. HHTT
  5. HTHH
  6. HTHT
  7. HTTH
  8. HTTT
  9. THHH
  10. THHT
  11. THTH
  12. THTT
  13. TTHH
  14. TTHT
  15. TTTH
  16. TTTT

Step 2: Identify the outcomes where at least three coins land facing tails up.

These are:

  1. HTTT
  2. THTT
  3. TTHT
  4. TTTH
  5. TTTT

Step 3: Calculate the probability.

The probability of an event is the number of ways that event can occur divided by the total number of outcomes.

So, the probability that at least three coins land facing tails up is 5 (the number of outcomes where at least three coins land facing tails up) divided by 16 (the total number of outcomes), or 5/16.

This problem has been solved

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