How to do binomial and Poisson probabilities (pdf and cdf) on the Casio fx-CG50
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
The binomial distribution and binomial hypothesis tests (critical regions) in A Level Statistics and IAL S1/S2; Poisson in Further Statistics and IAL S2.
Practise it: Statistical distributions · Hypothesis testing.
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).
- 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.
- 2nd vars (DISTR).
- Exactly: A: binompdf( trials 12, p 0.3, x value 4. Cumulative: B: binomcdf( 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: C: poissonpdf(λ, x) and D: poissoncdf(λ, x), 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 not allowed in IB, A Level or IGCSE exams.
- 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).
Binomial and Poisson distributions on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 7 (Distribution): 4 Binomial PD, 5 Binomial CD, 6 Poisson PD, 7 Poisson CD. Choose Variable.
- Binomial PD: x 4, N 12, p 0.3. Binomial CD gives P(X ≤ x).
- Poisson PD/CD: x and λ.
- For ≥, > and "between", rewrite with ≤ first, as on the TI-84.
Binomial and Poisson distributions on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Distribution → Binomial PD / Binomial CD / Poisson PD / Poisson CD → Variable.
- Enter x, N and p (or x and λ) and EXE. CD gives P(X ≤ x).
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.
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.
Do it in Desmos
Not in the exam. Desmos is not allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- 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.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
B=binomialdist(12,0.3)B.pdf(4)B.cdf(4)B.cdf(2,5)P=poissondist(3.5)P.cdf(2)
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.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions 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. Worked-example answers were recomputed independently in Python.