Multiple choice

A player tosses two coins. He wins $Rs.1$ if one head appears, $Rs.2$ if two heads appear. But he loss $Rs.5$. if two tail appears. The sum of the prize money is,

  1. $\dfrac {1}{2}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{-1}{4}$
  4. $\dfrac{1}{5}$
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C Correct answer
Explanation

Outcomes: HH (1/4), HT/TH (2/4), TT (1/4). Expected value = (1/4 * 2) + (2/4 * 1) + (1/4 * -5) = 0.5 + 0.5 - 1.25 = -0.25 = -1/4.

AI explanation

The expected value of the prize money is calculated by multiplying each outcome's prize by its probability and summing the results. The probabilities for getting one head, two heads, and two tails are 2/4, 1/4, and 1/4 respectively. Thus, the expected sum is (2/4 * 1) + (1/4 * 2) + (1/4 * -5), which equals 1/2 + 1/2 - 5/4, resulting in -1/4.

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