Multiple choice

Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the two top faces show the same colour is 1/2. Number of red faces on the second cube, is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cube 1: 5 red, 1 blue. Cube 2: x red, (6-x) blue. P(same color) = P(RR) + P(BB) = (5/6 * x/6) + (1/6 * (6-x)/6) = 1/2. (5x + 6 - x) / 36 = 1/2. 4x + 6 = 18. 4x = 12. x = 3.

AI explanation

Let the number of red faces on the second cube be x, making its blue faces 6 minus x. The probability of both top faces matching is the sum of the probabilities of both being red and both being blue, giving the equation (5/6)(x/6) + (1/6)((6 minus x)/6) = 1/2. Solving this equation yields 5x + 6 minus x = 18, so 4x = 12, which means x is 3.

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