A popular game show begins with the host reading a question to the contestants. One question involves putting 4 events (A, B, C, and D) in chronological order. What is the probability that the contestant gets the question correct is he or she just guesses?
Recently I asked this question and was given the answer 1/4. When I did it I used 1/4 *1/3*1/2* 1/1= 1/24 I was also told to solve using 4!= 24 So which way is right and when do I know what way to use. Why is it 1/4 instead. Please can some one explain I' so confused.
1/4! = 1/24=1/4*1/3*1/2*1/1
The above is in fact of randomly putting four events in the right order. It is not 1/4.
When considering the probability of getting a question correct by just guessing, you can either think in terms of the individual events or the overall order of the events. Let's break it down:
1. Probability using individual events: In this approach, you calculate the probability of getting each event correct individually and then multiply them together. Since there are four events (A, B, C, and D), and each event has an equal chance of being in any position, the probability of getting the first event correct is 1/4, the second event is 1/3, the third event is 1/2, and the fourth event is 1/1. Multiplying these probabilities together gives you (1/4) * (1/3) * (1/2) * (1/1) = 1/24. So, according to this approach, the probability of getting the entire sequence correct is 1/24.
2. Probability using overall order: In this approach, you consider the overall order of the events. Since there are four events, there are 4! (4 factorial) possible arrangements of these events in chronological order. So, there are 24 different possibilities. If the contestant is randomly guessing, only one of these 24 arrangements will be the correct order. Therefore, the probability of guessing the correct order is 1/24.
Now, you mentioned being told the answer is 1/4. The reason for this discrepancy is that the question is asking for the probability of getting the question correct, not the probability of guessing the entire sequence correctly. Since there is only one correct order out of the four possible orders (A, B, C, D), the probability of getting the entire question correct is indeed 1/4.
To summarize, if you are asked for the probability of getting a specific order correct, you calculate it as 1/24. But if you are asked for the overall probability of guessing the entire question correctly, you consider that there is only one correct order out of four possible orders, resulting in a probability of 1/4.