Binomial probabilities

Find the chance of getting exactly a certain number of successes in a fixed number of tries.

Use the binomial model when you repeat the same yes-or-no trial a fixed number of times, and each trial has the same chance of success. Think of flipping a coin or checking whether products pass a test.

The example: flip a fair coin 10 times. What is the chance of exactly 3 heads? It is 0.1171875 (about 11.7 percent).

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

Open the DISTR menu (2nd then vars) and pick binompdf( with the alpha key and A.
2ndDISTRvarsalphaAmath
Fill in trials 10, probability 0.5 and x value 3. Press down after each.
10▼0.5▼3▼
Select Paste, then press enter to calculate.
enterenter

You should seebinompdf(10,0.5,3) .1171875

binomcdf( (option B) adds up every outcome from 0 successes to x.

Classic Graphing 84 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

Open the Distribution mode and choose Binomial PD.
MENU74
Answer the prompts: x 3, N 10, p 0.5. Press = after each.
3=10=0.5=

You should seeBinomial PD p=0.1171875

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

Open the Stat mode, then DIST (F5), then BINM (F5), and choose Bpd (F1).
MENU2F5F5F1
Fill in x 3, Numtrial 10, p 0.5, pressing EXE after each. Press EXE once more to run it.
3EXE10EXE0.5EXEEXE

You should seeBinomial P.D p=0.1171875

Natural Color Graphing key reference

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

Type binomPdf( by hand, then the trials, the success chance and the count.
binompdf(10,0.5,3)
Press enter.
enter

You should seebinompdf(10,0.5,3) 0.117188

Classic CAS key reference

Tips

PDF means "exactly this many". CDF means "this many or fewer". For "at least", subtract a CDF from 1.
The tries must be independent: one result must not change the chance of the next.