Multiple choice

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

  1. $25$
  2. $41$
  3. $22$
  4. $42$
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D Correct answer
Explanation

The total outcomes for 6 coins is 2^6 = 64. We want at most 3 heads (0, 1, 2, or 3 heads). This is the sum of combinations: C(6,0) + C(6,1) + C(6,2) + C(6,3) = 1 + 6 + 15 + 20 = 42.

AI explanation

Using the binomial probability formula, the total possible outcomes when tossing six fair coins is 2^6 = 64. The number of outcomes with at most three heads is the sum of getting 0, 1, 2, or 3 heads, calculated as 6C0 + 6C1 + 6C2 + 6C3 = 1 + 6 + 15 + 20 = 42. Therefore, there are exactly 42 such outcomes.

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