Im not good at probability.
If there are 3 choices, and 3 people can choose any of them, what are the odds of the 3 people choosing all different choices?
There are 3! = 6 ways to assign the possible choices that are all different to the persons. The total number of choices, irrespective if they are all different or not, is 3^3 = 27.
The persons are randomly sampling from the set of 27 total choices, the probability that such a choice belongs to the subset of 6 that are all different is thus 6/27 = 2/9.
Each person has a 1/3 probability of making the choice from 3.
The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
so is it 1/27?
what if this is a game, and we play like 4 rounds? Would it be 2/9 ^4?
Each game is independent so yes.
To calculate the odds of three people choosing all different choices out of three options, we first need to determine the total number of possible outcomes. Since each person has three options, the total number of outcomes is obtained by multiplying the number of options for each person together: 3 x 3 x 3 = 27.
Now, let's calculate the number of favorable outcomes, which represent the scenarios where each person chooses a different choice.
For the first person, they can choose any of the three options freely, so there are 3 choices for the first person.
For the second person, once one option has been chosen by the first person, there are only 2 remaining options available. Therefore, there are 2 choices for the second person.
Similarly, for the third person, after the choices by the first two people, there is only 1 remaining option left. Hence, there is only 1 choice for the third person.
To determine the number of favorable outcomes, we multiply the number of choices for each person together: 3 x 2 x 1 = 6.
Now, we have both the total number of outcomes (27) and the number of favorable outcomes (6). To calculate the odds, we divide the number of favorable outcomes by the total number of outcomes: 6 / 27 = 2/9.
Therefore, the odds of all three people choosing different choices are 2/9.