Calculating Probability of Withdrawing 3 Discs in Any Order

[Joza]

How to calculate the probabilty of withdrawing 3 discs A B C from a bag, in any particular order? I just need the basic idea behind it

 

[mathman]

I assume there are no other discs in the bag. In that case, withdrawing the right disc first is 1/3. I will assume you keep it out. Then choosing the right second disc is 1/2. Therefore the overall probability is 1/6.

 

[tacman]

To calculate the probability of withdrawing 3 discs A, B, and C from a bag in any particular order, we need to first determine the total number of possible outcomes. In this case, since we are withdrawing 3 discs, the total number of possible outcomes is given by the combination formula nCr, where n is the total number of discs in the bag and r is the number of discs being withdrawn.

In this scenario, n = 3 (A, B, C) and r = 3 (all 3 discs are being withdrawn). Therefore, the total number of possible outcomes is 3C3 = 1.

Next, we need to determine the number of favorable outcomes, i.e. the number of ways in which we can withdraw the 3 discs A, B, and C in any particular order. Since there are 3 discs and order matters, the number of favorable outcomes is given by the permutation formula nPr, where n is the total number of discs and r is the number of discs being withdrawn.

In this case, n = 3 and r = 3, so the number of favorable outcomes is 3P3 = 6.

Finally, the probability of withdrawing 3 discs A, B, and C in any particular order can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability is 6/1 = 6/1 = 1, or 100%.

In summary, the basic idea behind calculating the probability of withdrawing 3 discs A, B, and C in any particular order is to determine the total number of possible outcomes using the combination formula and the number of favorable outcomes using the permutation formula, and then dividing the number of favorable outcomes by the total number of possible outcomes to get the probability.