Multiple choice

From 80 cards numbered 1 to 80, two cards are drawn at random. The probability that the cards have the numbers divisible by 4 is

  1. $\displaystyle \frac{15}{316}$
  2. $\displaystyle \frac{17}{316}$
  3. $\displaystyle \frac{19}{316}$
  4. $\displaystyle \frac{21}{316}$
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C Correct answer
Explanation

Numbers divisible by 4 between 1 and 80 are 80/4 = 20 numbers. The probability of picking two such numbers is (20/80) * (19/79) = (1/4) * (19/79) = 19/316.

AI explanation

To find the probability, divide the number of ways to choose two cards divisible by 4 by the total ways to choose any two cards. There are exactly 20 numbers divisible by 4 between 1 and 80, so the favourable combinations are 20C2, which equals 190. The total combinations of two cards from 80 is 80C2, which equals 3160. The resulting probability fraction is 190/3160, which simplifies by dividing the numerator and denominator by 10 to obtain 19/316.

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