On a TI-84 Plus CE
- Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1).
- 2nd → DISTR → binompdf(n, p, r) or binomcdf(n, p, r).
Tip: ‘Fewer than 3’ means X ≤ 2, so use the cdf at 2, not 3.
Binomial distribution
Handles 'exactly', 'at most' and 'at least' for B(n, p) without expanding anything.
In short: The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. The GDC's binomial pdf gives P(X = k) and its cumulative function gives P(X ≤ k). Enter the number of trials n, the probability p and the value k, and choose the right function.
When you'd use this
- A fixed number of independent trials, each with the same probability of "success".
- A question asks for P(X = k), P(X ≤ k) or P(X ≥ k) for a binomial variable.
- Avoiding expanding (p + q)ⁿ by hand for "exactly", "at most" or "at least" questions.
- Finding an expected number of successes, np, before answering a follow-up question.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | 2nd → DISTR → binompdf(n, p, r) or binomcdf(n, p, r). | Statistics menu → DIST (F5) → BINM (F5) → Bpd or Bcd. | menu → Statistics → Distributions → Binomial Pdf / Binomial Cdf. |
On a Casio fx-CG50 and fx-CG100
- Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1).
- Statistics menu → DIST (F5) → BINM (F5) → Bpd or Bcd.
Tip: ‘Fewer than 3’ means X ≤ 2, so use the cdf at 2, not 3.
On a TI-Nspire CX
- Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1).
- menu → Statistics → Distributions → Binomial Pdf / Binomial Cdf.
Tip: ‘Fewer than 3’ means X ≤ 2, so use the cdf at 2, not 3.
Related guides
Try it yourself
Here's a real IB-style question that uses exactly this technique.
Medium
Calculator
Paper 2
[3 marks]
X ~ B(12, 0.3). Find (a) P(X = 4) and (b) P(X ≤ 4), each to 3 significant figures.
(a) 0.231 (b) 0.724
Mark it
Correct
3 / 3 marks
Worked solution & mark scheme:
M1 binompdf(12, 0.3, 4) and binomcdf(12, 0.3, 4)
A1 P(X = 4) = 0.231
A1 P(X ≤ 4) = 0.724
Common questions
When would I need to find binomial probabilities in IB Maths?
Handles 'exactly', 'at most' and 'at least' for B(n, p) without expanding anything. A fixed number of independent trials, each with the same probability of "success". A question asks for P(X = k), P(X ≤ k) or P(X ≥ k) for a binomial variable.
How do I find binomial probabilities on a TI-84 Plus CE?
1. Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1). 2. 2nd → DISTR → binompdf(n, p, r) or binomcdf(n, p, r).
How do I find binomial probabilities on a Casio fx-CG50 and fx-CG100?
1. Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1). 2. Statistics menu → DIST (F5) → BINM (F5) → Bpd or Bcd.
How do I find binomial probabilities on a TI-Nspire CX?
1. Translate the words: exactly r → pdf; at most r → cdf; at least r → 1 − cdf(r−1). 2. menu → Statistics → Distributions → Binomial Pdf / Binomial Cdf.
What should I watch out for when I find binomial probabilities?
‘Fewer than 3’ means X ≤ 2, so use the cdf at 2, not 3.
How are marks awarded when I find binomial probabilities in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: M1: binompdf(12, 0.3, 4) and binomcdf(12, 0.3, 4); A1: P(X = 4) = 0.231; A1: P(X ≤ 4) = 0.724.
Practise with your calculator
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.