Multiple choice

One lottery ticket is drawn at random from a bag containing $20$ tickets numbered from $1$ to $20$. Find the probability that the number drawn is either even or square of an integer:

  1. $\dfrac14$
  2. $\dfrac45$
  3. $\dfrac35$
  4. $\dfrac15$
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C Correct answer
Explanation

The total number of possible outcomes is 20. The even numbers in this range are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} (10 numbers), and the perfect squares are {1, 4, 9, 16}. Combining these two sets without duplication gives {1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20}, which contains 12 numbers. Thus, the probability is 12/20 = 3/5.

AI explanation

There are 10 even numbers and 4 perfect squares (1, 4, 9, 16) between 1 and 20. Using the addition rule of probability, the total favorable outcomes is 10 plus 4 minus 2, since 4 and 16 are both even and perfect squares, leaving 12 favorable outcomes. The probability is 12 divided by 20, which simplifies to 3/5. The result is 3/5.

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