Multiple choice

In a game, a participant pays Rs. 20 to roll a dice. If he gets a prime number, he wins Rs. 30, if he gets a composite number, he loses his money, and if he gets neither a prime nor a composite number, he wins Rs. 50. What is his average profit percentage?

  1. 10%

  2. 16.66%

  3. 20%

  4. 25%

  5. 33.33%
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B Correct answer
Explanation

Prime numbers on a die are 2, 3, 5 (3 outcomes). Composite numbers are 4, 6 (2 outcomes). Neither is 1 (1 outcome). Expected value = (3/6 * 30) + (2/6 * -20) + (1/6 * 50) - 20 = 15 - 6.66 + 8.33 - 20 = -3.33. The profit percentage is calculated on the investment of 20, resulting in 16.66% profit.

AI explanation

The outcomes of rolling a die are 1, 2, 3, 4, 5, and 6; the prime numbers are 2, 3, and 5, the composite numbers are 4 and 6, and 1 is neither. For primes, the player pays 20 and wins 30, netting a 10 profit; for composites, the player loses the 20 paid; for 1, the player pays 20 and wins 50, netting a 30 profit. The expected return per game is ((3 * 10) + (2 * -20) + (1 * 30)) / 6 = (30 - 40 + 30) / 6 = 20 / 6 = 3.33. The average profit percentage on the Rs. 20 cost is (3.33 / 20) * 100 = 16.66%.

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