Question

Terrence is playing a game in which he will randomly select one square tile and one round tile from the tile sets shown below. Before he does so, he tries to guess which tiles he will draw.
Square tiles: 12 blue, 20 yellow, 8 red, 6 green, 4 pink, 5 black, 3 brown, 2 white.Round tiles: 9 black, 4 green, 3 yellow, 2 white, 6 blue, 12 red.
Of the four possible guesses listed below, which will give Terrence the highest chance of success?
a.
black or pink square tile and blue or green round tile
b.
yellow square tile and yellow round tile
c.
green, brown, or white square tile and black or white round tile
d.
red square tile and red or white round tile

Answer 1

Total square tiles = 12+20+8+6+4+5+3+2 = 60.
Total round tiles = 9+4+3+2+6+12 = 36.

Compute each guess probability = (probability of square choice) × (probability of round choice).

a) (black or pink) = (5+4)/60 = 9/60. (blue or green) = (6+4)/36 = 10/36.
P(a) = 9/60 × 10/36 = 90/2160 = 1/24 ≈ 0.04167.

b) yellow = 20/60 = 1/3. yellow round = 3/36 = 1/12.
P(b) = 1/3 × 1/12 = 1/36 ≈ 0.02778.

c) (green, brown, or white) = (6+3+2)/60 = 11/60. (black or white) = (9+2)/36 = 11/36.
P(c) = 11/60 × 11/36 = 121/2160 ≈ 0.05602.

d) red = 8/60. (red or white) = (12+2)/36 = 14/36.
P(d) = 8/60 × 14/36 = 112/2160 = 7/135 ≈ 0.05185.

Highest probability is (c).