How to do binomial and Poisson probabilities (pdf and cdf) on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
On the fx-CG50: MENU → 2 (STATISTICS) → F5 (DIST) → F5 (BINOMIAL) → F1 (Bpd).On the TI-84 Plus CE: 2nd vars (DISTR).On the TI-Nspire CX II: menu → Probability → Distributions → Binomial Pdf.
P(X = r) and P(X ≤ r) for B(n, p) and Po(λ), and how to turn ≥, > and "between" into what the calculator does. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
Binomial in AA and AI (SL and HL); Poisson in AI HL only (it is not in the AA syllabus). Typical Paper 2 parts: "exactly", "at most", "at least" and "between" probabilities, and the expected number. Define the distribution (X ~ B(12, 0.3)) before you use it.
Practise it: SL AA binomial · SL AI probability distributions · HL AA binomial · HL AI Poisson.
Which IB course and paper
| Course | GDC papers | What you use it for |
|---|---|---|
| AA SL | Paper 2 (Paper 1 is calculator-free) | Binomial only. |
| AA HL | Papers 2 and 3 (Paper 1 is calculator-free) | Binomial only (the Poisson distribution is in the AI HL syllabus, not AA). |
| AI SL | Papers 1 and 2 | Binomial only. |
| AI HL | Papers 1, 2 and 3 | Binomial and Poisson. |
A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.
Topic notes: Binomial distribution (AA SL) · Binomial distribution (AA HL) · Normal and Poisson distributions (AI HL).
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Binomial and Poisson distributions on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
Watch the key presses on the fx-CG50Binomial pdf · Binomial cdf
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- MENU 2 (STATISTICS), F5 (DIST), then F5 (BINOMIAL). For Poisson: F6 (▷) F1 (POISSON).
- Exactly: F1 (Bpd). Data: Variable, x 4, Numtrial 12, p 0.3, Execute.
- Cumulative: F2 (Bcd). Data: Variable, Lower 0, Upper 4, Numtrial 12, p 0.3, Execute. For P(X ≥ 5) use Lower 5, Upper 12; for P(2 ≤ X ≤ 5) Lower 2, Upper 5.
- Poisson: F1 (Ppd) with x and μ (= λ = 3.5), or F2 (Pcd) with Lower, Upper and μ.
- Because the fx-CG50's Bcd and Pcd take a Lower and an Upper value, you rarely need the 1 − P(…) step. (Older Casio models only ask for x and give P(X ≤ x).)
- Data: List works out several x values at once from a list.
- InvB (F3) finds the smallest x with P(X ≤ x) ≥ a given value: useful for critical regions.
Binomial and Poisson distributions on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
Watch the key presses on the TI-84 Plus CE6 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 2nd vars (DISTR).
- Exactly: scroll down the DISTR list to binompdf( and fill in trials 12, p 0.3, x value 4. Cumulative: binomcdf( (the next item) gives P(X ≤ x).
- At least / more than: P(X ≥ 5) = 1 − binomcdf(12, 0.3, 4). Between: P(2 ≤ X ≤ 5) = binomcdf(12, 0.3, 5) − binomcdf(12, 0.3, 1).
- Poisson: poissonpdf(λ, x) and poissoncdf(λ, x), just below binomcdf( in the same list, work the same way.
- binomcdf is always P(X ≤ x): write the inequality in that form first.
Binomial and Poisson distributions on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS (the CX II CAS is a different model: check the exam rules before using one).
- Calculator page: menu → Probability → Distributions → Binomial Pdf or Binomial Cdf.
- Binomial Cdf asks for n, p, a lower bound and an upper bound: P(2 ≤ X ≤ 5) = binomCdf(12, 0.3, 2, 5).
- Poisson Pdf / Poisson Cdf: λ, then x (or the lower and upper bounds).
For teachers: Show on the board Print a keystroke card Teaching GDC skills
Worked example
X ~ B(12, 0.3). Find P(X = 4), P(X ≤ 4), P(X ≥ 5) and P(2 ≤ X ≤ 5). Y ~ Po(3.5). Find P(Y = 2), P(Y ≤ 2) and P(Y > 4).
Answers (checked with Python)
P(X = 4) = 0.231140, P(X ≤ 4) = 0.723655, P(X ≥ 5) = 1 − P(X ≤ 4) = 0.276345, P(2 ≤ X ≤ 5) = 0.797126. P(Y = 2) = 0.184959, P(Y ≤ 2) = 0.320847, P(Y > 4) = 1 − P(Y ≤ 4) = 0.274555.
Now try it on an exam-style question
Use the keystrokes above on IB-style probability distributions questions. Free to try, no sign-up.
Common calculator mistakes
- P(X ≥ 5) is 1 − P(X ≤ 4), not 1 − P(X ≤ 5).
- Using the pdf (exactly) when the question says "at most" or "at least".
- Swapping n and p, or typing p as a percentage (30 instead of 0.3).
- Poisson with the wrong interval: 3.5 per hour means λ = 7 for two hours.
- Not stating the distribution: "X ~ B(12, 0.3)" earns the method mark.
- Writing "binomcdf" as your working: write P(X ≤ 4) with X ~ B(12, 0.3) instead.
- Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).
If you get an error
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Is every value allowed? σ must be positive and p must be between 0 and 1. A value typed into the wrong box (σ where μ goes) can do it too. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:SYNTAX, ERR:ARGUMENT
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
ERR:ARGUMENT A function or instruction does not have the correct number of arguments (inputs). Check: A distribution command with an input missing: normalcdf( needs lower, upper, μ and σ. Fix: Give every argument, separated by commas.
TI-Nspire CX II: Domain error, Syntax error, Too few arguments / Too many arguments
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
Too few arguments / Too many arguments The function or command was given fewer (or more) arguments than it needs. Check: A distribution or statistics command with a value missing or an extra comma. Fix: Give exactly the arguments the command needs.
Do it in Desmos
Not in the exam. Desmos is not an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- B = binomialdist(12, 0.3) draws the bar chart.
- B.pdf(4) is P(X = 4); B.cdf(4) is P(X ≤ 4); B.cdf(2, 5) is P(2 ≤ X ≤ 5).
- P = poissondist(3.5) works the same way.
Open desmos.com/calculator (free, in any browser) and type:
B=binomialdist(12,0.3)B.pdf(4)B.cdf(4)B.cdf(2,5)P=poissondist(3.5)P.cdf(2)
Questions
Can I use a calculator for binomial and Poisson distributions in the exam?
In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.
What are the fx-CG50 keystrokes for binomial and Poisson distributions?
MENU 2 (STATISTICS), F5 (DIST), then F5 (BINOMIAL). For Poisson: F6 (▷) F1 (POISSON). Then Exactly: F1 (Bpd). Data: Variable, x 4, Numtrial 12, p 0.3, Execute. Then Cumulative: F2 (Bcd). Data: Variable, Lower 0, Upper 4, Numtrial 12, p 0.3, Execute. For P(X ≥ 5) use Lower 5, Upper 12; for P(2 ≤ X ≤ 5) Lower 2, Upper 5. The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the models shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.