How to Solve a Binomial Distribution Problem Using the Binomial Formula

binomial distribution 8 Comments

The binomial  formula–used to calculate the probability of success for binomial distributions–isn’t the easiest of formulas to work . If you use a Ti-83 or Ti-89, much of the work is done for you. However, if you don’t own one, here are the simple steps you should follow to get the answer right every time.  

binomialprobabilityformula

Sample question: “60% of people who purchase sports cars are men.  If 10 sports car owners are randomly selected, find the probability that exactly 7 are men.”

Step 1:: Identify ‘n’ and ‘X’ from the problem. Using our sample question, n (the number of randomly selected items — in this case, sports car owners are randomly selected) is 10,  and  X (the number you are asked to “find the probability” for) is 7.

Step 2: Figure out the first part of the formula, which is:

n! / (n – X)!  X!

Substituting the variables:

10! / ((10 – 7)! × 7!)

Which equals 120. Set this number aside for a moment.

Step 3: Find “p” the probability of success and “q” the probability of failure. We are given p = 60%, or .6. therefore, the probability of failure is 1 – .6 = .4 (40%).

Step 4: Work the next part of the formula.

pX
= .67
= .0.0279936

Set this number aside while you work the third part of the formula.

Step 5: Work the third part of the formula.

q(.4 – 7)
= .4(10-7)
= .43
= .0.064

Step 6: Multiply the three answers from steps 2, 4 and 5 together.
120  × 0.0279936 × 0.064 = 0.215.

That’s it!

Related posts:

  1. How to Work a Binomial Distribution Formula
  2. Using the Normal Approximation to solve a Binomial Problem
  3. How to read a binomial distribution table
  4. How to solve a question about probability frequency distribution
  5. How to find the mean: probability distribution or binomial distribution
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8 Responses to “How to Solve a Binomial Distribution Problem Using the Binomial Formula”

  1. How to Do Everything Statistics » How to read a binomial distribution table said:

    Sep 25, 09 at 8:34 am

    [...] How to use the binomial formula to solve a binomial problem. [...]

  2. Mary Johnson said:

    Sep 25, 09 at 2:51 pm

    This helped me so much. It is starting to make sense. Thanks!

  3. Angie Widdows said:

    Oct 01, 09 at 10:05 am

    To someone not studying the examples in MathZone, this is a great example. I really try to follow the examples I see on-line and this example mirror’s that. It was helpful.

  4. Vanessa DuBarry said:

    Oct 01, 09 at 10:54 am

    TO ME THIS QUESTION IS REALLY DIFFICULT TO UNDERSTAND, WHEN I WAS DOING THIS PROBLEM ON MATHZONE I COULDNT FIGURE IT OUT , AND THE WORST PART WAS THAT WHEN YOU CLICK THE SHOW ME BUTTON IT DOESNT EXPLAIN ANYTHING, SO FOR ME TO BE ABLE TO HAVE THIS SORT OF EXPLANATIONS AND STEP BY STEP PROBLEMS REALLY HELP, I AM STILL HAVING A BIT OF A TROUBLE BECAUSE JUST BY LOOKING AT THE PROBLEM AND SEEING THAT EXCLAMATION MARK IN IT MAKES ME SO CONFUSED. WHAT DOES THAT REALLY MEAN?

  5. Stephanie said:

    Oct 04, 09 at 8:25 am

    It’s a factorial.

    Stephanie

  6. Scott Selph said:

    Oct 05, 09 at 6:42 am

    This made for a very difficult problem solver. There was to much to keep up with. In my google search I was able to find a table and was able to make that work. But the binomial calculator is still much easier.

  7. Stephanie said:

    Oct 06, 09 at 2:29 am

    Hi Scott,
    There are some tables on this site (look up the top, under “tables”) but you are correct–the calculator is much easier!!
    Stephanie

  8. Gina said:

    Oct 12, 10 at 9:07 pm

    The step by step for binomial distribution was very helpful. However, I am running into a lot of problems on homework that read “atleast 1″ or “3 or more” instead of just saying “exactly 3.” Is there anything on this website that might be able to explain that to me?

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