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 6 people, and there are 6 different possible weapons and 9 possible rooms. At one point in the game, you have narrowed the possibilities down to 2 people, 3 weapons, and 4 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? Enter a fraction or round your answer to 4 decimal places, if necessary.

Answer 1

1/24

Explanation:

To start, we can calculate the probability of each individual event:

Getting the person right:

1/2

Getting the weapon right:

1/3

Getting the room right:

1/4

Here, you're trying to find the probability of the intersection of the three events. This means we must multiply the probabilities of the independent events together.

1/2*1/3*1/4=1/24

or

0.0417

Note that we multiply the probabilities together when the previous event doesn't affect the probability of the next event. In general, questions that ask for the probability of a happening and b happening mean you multiply the probability of a and b (events that satisfy your demands are decreasing because you need BOTH events to occur).

On the other hand, questions that ask for the probability of a or b happening, meaning the events that satisfy your demands will increase (2 options versus 1), so you'd add the probabilities of a and b happening.

Hope that makes sense, let me know if you have any questions!