Question

You are playing a game in which you randomly select one square tile and one round tile from the sets shown below. Before you select your tiles, you try to guess which combination you will pick.
20 green square tiles, 9 red square tiles, 16 pink square tiles, 10 yellow square tiles, 5 blue square tiles.Circle tiles: 5 purple, 6 orange, 10 blue, 1 white, 2 yellow, 4 red, 5 black, 3 green.
Of the four possible guesses listed below, which one will give you the greatest chance of success?
a.
green square tile and red round tile
b.
pink square tile and orange or yellow round tile
c.
red or blue square tile and black or green round tile
d.
blue square tile and blue or purple or white round tile

Answer 1

Total pairs = 60 square tiles × 36 round tiles = 2160 equally likely combinations.

Compute favorable combinations for each guess:

a. green square and red round: 20 × 4 = 80 → 80/2160 = 1/27 ≈ 0.0370
b. pink square and orange or yellow round: 16 × (6+2) = 16 × 8 = 128 → 128/2160 = 8/135 ≈ 0.0593
c. red or blue square and black or green round: (9+5) × (5+3) = 14 × 8 = 112 → 112/2160 = 7/135 ≈ 0.0519
d. blue square and blue or purple or white round: 5 × (10+5+1) = 5 × 16 = 80 → 80/2160 = 1/27 ≈ 0.0370

Largest probability is option b.