A popular game show begins with the host reading a question to the contestants. One question involves putting four events (A, B, C and D) in chronological order. What is the probability that the contestant gets the question correct if he or she just guesses?
1 in four or one fourth
Consider
ABCD
BCDA
CDAB
DABC
DCBA
CBAD
Etc.
Any of the 4 could be in the first position. Once that position is filled, any of the remaining three could hold the second position, and so on.
So there are 4! ("four factorial") orders (4 * 3 * 2 * !) = 24
To find the probability that the contestant gets the question correct if they just guess, we first need to determine the number of possible ways the four events can be arranged. Since there are four events (A, B, C, and D), there are 4! (4-factorial) ways to arrange them.
The formula for factorial is n! = n * (n-1) * (n-2) * ... * 2 * 1
So, 4! = 4 * 3 * 2 * 1 = 24.
Out of these 24 possible arrangements, only one arrangement is the correct chronological order. Therefore, the contestant has a 1 in 24 chance of guessing correctly.
Hence, the probability that the contestant gets the question correct if they just guess is 1/24 or approximately 0.042 (or 4.2%).