Daily Dose 034 | Probability and Statistics
How do you calculate the probability of Combinations?
Knowing how to calculate the probability of Combinations can be a tricky endeavor.
Often confused with Permutations, without a doubt, come exam day, you are going to see a problem (or problems) that will require you to form subsets of a larger group of items.
So will this be a win for you?
At Prepineer, we are going to make sure that it is.
In this video, we dive into a FE Exam Practice Problem in the subject of PROBABILITY AND STATISTICS, specifically learning how to find the number of COMBINATIONS of given a set of objects.
What is a COMBINATION?
A COMBINATION is a selection of objects where the order doesn’t matter.
For example, say we have three balls: one red, one white, and one blue.
If we wanted to see how many different variations of these balls we get after choosing 2 at a time, we find that we get:
red – white
red – blue
white – blue
white – red
blue – red
blue – white
But since order doesn’t matter, red – white and white – red are the same.
So that’s a single combination, which goes for the others as well.
So in reality, instead of 6, there are 3 COMBINATIONS.
From a textbook sense, we would first find the number of PERMUTATIONS (which is 6 for the above scenario) and divide it by the number of ways we can rearrange the PERMUTATIONS…meaning, pair them up as white – blue : blue-white, etc.
So if you are wondering…
How can I calculate the probability of Combinations?
Generally, use the following process to calculate the probability of Combinations.
- Step 1: Determine the number of items in the sample space (total number of possible outcomes)
- Step 2: Determine the number of items in the event space (the number of outcomes that satisfy the condition of interest)
- Step 3: Use the formula for calculating the number of combinations:
- Step 4: Plug in the values from Steps 1 and 2 into the formula from Step 3 to calculate the number of combinations.
- Step 5: Calculate the probability of the event by dividing the number of combinations by the total number of possible outcomes:
P(event) = number of combinations / total number of possible outcomes.
n C r = n! / r!(n-r)!
Where n is the total number of items, r is the number of items in the event space, and ! denotes the factorial function.
Check out the video and see how we can go about solving this type of problem in the most efficient manner.
As always, with Love, Prepineer
[VIDEO] How to calculate the probability of Combinations?
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