How can you tell when you need to use the binomial coefficient for probabilities?

klastiesym

klastiesym

Answered question

2022-10-21

How can you tell when you need to use the binomial coefficient for probabilities?
For example, the probability of being dealt a hand with 3 spades and 2 hearts from a standard deck of cards. I would think the geometric probability is:
13 12 11 13 12 52 51 50 49 48 because I usually don't use the binomial coefficient with geometric probabilities, but the answer is incorrect unless I multiply by the binomial coefficient (which is a factor of 10 here).

Answer & Explanation

Kason Gonzales

Kason Gonzales

Beginner2022-10-22Added 15 answers

Step 1
If X is a binomial random variable with parameters n, p then it's probability mass function is given by P ( X = k ) = ( n k ) p k ( 1 p ) n k for all 0 k n. The binomial coefficient ( n k ) counts the possible ways to get k successful results in the total of the n trials.
For example if n = 10 and k = 2, then you can obtain the two successes in trials 1 and 2, or in trials 1 and 3 or in trials 7 and 10 and so on. The binomial coefficient counts exactly all these possibilities and therefore it can't be omitted. It's value is equal to 1 when k = 1 or when k = n - as you pointed out - and thus these are the only cases in which it can be omitted.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?