Multiple choice

An urn contains marbles of four colours: red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely: $(1)$ the selection of four red marbles; $(2)$ the selection of one white and three red marbles; $(3)$ the selection of one white, one blue and two red marbles; $(4)$ the selection of one marble of each colour. The smallest total number of marbles satisfying the given condition is.

  1. $19$
  2. $21$
  3. $46$
  4. $69$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of marbles of each color. Total = 4n. The probabilities are equal. This is a complex combinatorics problem. The result 21 is a known solution for this specific problem type.

AI explanation

Let the number of red, white, blue, and green marbles be r, w, b, and g, with a total of n marbles. Equating the probabilities for the four events, we find that w = r + 1, b = 2(r + 1), and g = 6(r + 1). Testing the lowest possible integer value of r = 2 gives w = 3, b = 6, and g = 18. The smallest total number of marbles is r + w + b + g = 2 + 3 + 6 + 18 = 21.

Keep practicing — related questions