Question

Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 55 people, 55 weapons, and 66 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct

Answer 1

The probability of the guess being correct is 1/150.

Explanation:

The information provided for the game Clue is:

• Clue is a board game in which you must deduce three details surrounding a murder.
• The guilty person can be chosen from 6 people.
• There are 6 different possible weapons.
• There are 9 possible rooms.

Now it is provided that at some point the possibilities have been narrowed down to 5 people, 5 weapons, and 6 rooms.

The number of ways to select a guilty person from the 5 selected people is,

n (P) = 5

The number of ways to select a weapon from the 5 selected weapon is,

n (W) = 5

The number of ways to select a room from the 6 selected rooms is,

n (R) = 6

Then the total number of random guesses is,

N = n (P) × n (W) × n (R)

= 5 × 5 × 6

= 150

And only one of these 150 guesses is correct.

So, the probability of the guess being correct is 1/150.