## How to Work a Binomial Distribution Formula

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The binomial distribution formula can calculate the probability of success for binomial distributions. Often you’ll be told to “plug in” the numbers to the formula and calculate. This is easy to say, but not so easy to do–unless you are very careful with order of operations, you won’t get the right answer. If you have a Ti-83 or Ti-89, the calculator can do much of the work for you. If not, here’s how to break down the problem into simple steps so you get the answer right–every time.

Step 1:: Read the question carefully.  Sample question: “80% of people who purchase pet insurance are women.  If 9 pet insurance owners are randomly selected, find the probability that exactly 6 are women.”

Step 2:: Identify ‘n’ and ‘X’ from the problem. Using our sample question, n (the number of randomly selected items) is 9,  and  X (the number you are asked to find the probability for) is 6.

Step 3: Work the first part of the formula. The first part of the formula is

n! / (n – X)!  X!

9! / ((9 – 6)! × 6!)

Which equals 84. Set this number aside for a moment.

Step 4: Find p and q. p is the probability of success and q is the probability of failure. We are given p = 80%, or .8. So the probability of failure is 1 – .8 = .2 (20%).

Step 5: Work the second part of the formula.

pX
= .86
= .262144

Set this number aside for a moment.

Step 6: Work the third part of the formula.

q(n – X)
= .2(9-6)
= .23
= .008

Step 7: Multiply your answer from step 3, 5, and 6 together.
84  × .262144 × .008 = 0.176.

That’s it!

## 21 thoughts on “How to Work a Binomial Distribution Formula”

1. Scott Selph

This explains everything much simpler than the book. The step-by-step guidance is just what I needed. Thank You

2. angie widdows

Things get so confusing on when to subtract from 1 or to subtract from .5000. Is there any special reasoning or logic on which one to use.

3. crystal lydick

I keep getting so lost on step #3 , I never get the right answer to this portion of the problem. Can someone walk me through exactly what I am suppose to do at that point??? Thank you ih advance.

4. crystal lydick

Thanks John, This is driving me insane I cannot figure it out!! I have done terrible on the quiz. I have one more chance to take it, but I don’t know how to work 3 of the problems!! Hope you did better than I have!

5. diyana

i’m a bit confuse to differentiate the question for binomial distribution and the conditional probability. and which formula is suitable for the question.

6. Andale

Diyana,

Could you please post the question that you are confused about? That way I would be able to tell you which formula is most suitable.

Stephanie

7. Tee

Omgshhhh! I am stuck on step 4 & 5!
I have an exam for this on Friday so if anyone can help me before than please do!
On step 4 is 1 always the number for this? Even if it’s a different equation?
For example in my question P = 80, N = 6 and X = 4.
Basically I’d I did this equation does 1 change for this?

Step 5 threw me off as I’m using the IPhone calculator and don’t have a statistical calculator,
I get the 8 but what’s the little 6 for? And where is it on the calculator? What button do i press to get = .262144.

And also would it vary from my equation?

8. michael Kirigo

9. Tyler

Hi there, i do believe that there might be a problem with the question as it states that the probability of women having the insurance is .80. what is the probability for 6 of the 9 to be women. you must use p=.80 do not subtract it from 1 as we are not interested in the other party.

Have a great day, cheers

10. Cpoteet44

Crystal, this step you’re having trouble with is the formula to find a combination. A simple way to find this is to use the combination button on a TI83 or TI84 calculator under the math–>probability button. You plug in n(total number of probabilities) first then hit nCr under probability and them plug in x. Once you find that, use the rest of the steps as suggested. I hope this helped and didn’t confuse you even more!

11. Syed Hassam Shah

Awesum i love the way of describe my all
Things remind because of these step love it hars off admin thanks alot

12. Vikrant Payal

If you get stuck on step 3, read this

The ! sign stands for factorial. It means multiplying the number behind it until the series reaches one. For example, 4! = 4*3*2*1