Multiple choice

Five fair coins are tossed simultaneously. In how many of the outcomes will at most 3 coins turn up as tails?

  1. 26

  2. 10

  3. 16

  4. 20

  5. None of these
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A Correct answer
Explanation

Total outcomes for 5 coins is 2^5 = 32. Outcomes with more than 3 tails are 4 tails (5C4 = 5) and 5 tails (5C5 = 1). Total outcomes with at most 3 tails = 32 - (5 + 1) = 26.

AI explanation

When five fair coins are tossed, the total number of outcomes is 2 to the power of 5, which equals 32. The number of outcomes with at most 3 tails includes the sums of combinations for exactly 0, 1, 2, and 3 tails. Using the combinations formula, we calculate 5C0 plus 5C1 plus 5C2 plus 5C3, which translates to 1 plus 5 plus 10 plus 10. The sum of these outcomes is 26.

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