Solve the problem.
-A ring contains 8 keys: 1 red, 1 blue, and 6 gold. If the keys are arranged at random on the ring, find the probability that the red is next to the blue.
A) .047
B).143
C) 25
D) .286

Question

Quizplus · Accepted Answer

To find the probability that the red key is next to the blue key, consider the red and blue keys as a single unit. This creates 7 units to arrange (6 gold keys + 1 red-blue pair). The number of ways to arrange 7 units in a circle is (7-1)! = 6!. Within the red-blue pair, the keys can be arranged in 2 ways (red-blue or blue-red). Therefore, the total number of favorable arrangements is 6! * 2. The total number of ways to arrange all 8 keys in a circle is (8-1)! = 7!. The probability is (6! * 2) / 7! = 2/7 ≈ 0.286.

Solve the Problem. -A Ring Contains 8 Keys: 1 Red, 1 Blue, and 1