How do probabilities work? How do you calculate them?

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Example: if four people need to be randomly assigned a task, and they decide to each draw some notes with the task’s name on them to decide who gets which task, how do probabilities work in this case? Would there be any difference in chances if there were just four notes with each task’s name on them compared to four bowls each containing all four people’s names and each one corresponding to a task? And you just draw one name from each bowl to see which person which corresponding task gets? If someone’s name is drawn twice, the second time the name is just put aside and the bowl is redrawn. Many more examples cuz I’m really confused, but this is one of the main ones that confuse me.

Edit: forgot to add something.

In: Mathematics

Well probability is based upon a desired outcome occuring.

It is usually a fraction. What you want to happen/possible things that might happen.

Your scenario would be /4.

Probability is a pretty broad topic, but the general basis is the number of possibilities you want compared to the total number of possibilities.

In your case, the total number of possibilities is 4 factorial, written as 4! Which basically means 4x3x2x1. If you wanted to find 7! You would do 7x6x5x4x3x2x1. Since you didn’t specify what possibilities you wanted, you can’t really use probabilities.

One bowl total would be different than 4 bowls, because if there is a different bowl for each task then it’s possible for one person to get multiple tasks or not get any tasks

For any simple probability the calculation is always:

(Total number of possible outcomes that you are interested in) ÷ (Total number of all possible outcomes)

Probability of drawing the Ace Spades from a normal deck of cards: 1/52

Probability of drawing any ten from a deck of cards: 4/52

Probability of drawing any heart from a deck of cards: 13/52

So in your first example, assuming that everyone’s name is in the bowl only once, everyone has a one in four (1/4) chance of being assigned any particular task.

In your example with multiple bowls, assuming that you dig through the other bowls and remove the name of whoever has already been assigned a task then the overall probability is the same.

That’s the probability at the start; but if you calculate it in between rounds of drawing then it changes, since the number of people and tasks have changed.