Multiple choice

When a coin is tossed in an experiment, the result is either a head or a tail. A head is given a point value of $1$ and a tail is given a point value of $-1$. If the sum of the point values after $50$ tosses is $14$, how many of the tosses must have resulted in heads?

  1. $14$
  2. $18$
  3. $32$
  4. $36$
  5. $39$
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C Correct answer
Explanation

Let H be heads and T be tails. H + T = 50. H - T = 14. Adding equations: 2H = 64, H = 32.

AI explanation

Let h be the number of heads, so the number of tails is 50 minus h. The total sum of the point values is 1 times h minus 1 times (50 minus h), which is given as 14. Solving the equation 2h minus 50 equals 14 gives 2h equals 64, so h equals 32. The result is 32.

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