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Compare exact, cumulative and interval event counts

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Step-by-step guide · read-only · Selected E2

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Data & tools
Task requirements

Enter separate formulas in E2:E6. B2 is the fixed number of independent trials, B3 the same event probability in every trial and B4 an exact count. E2 is P(X=B4); E3 is P(X<=B4); E4 is P(X>=B7); E5 is P(B5<=X<=B6), including both endpoints; E6 is the expected count. Keep probabilities as unrounded proportions. Preserve small nonzero tails rather than rounding them to zero.

Edit the event model

Apply one numeric value to the actual worksheet. Counts, proportions and interval boundaries keep their separate meanings. The complete model is validated before an edit replaces a valid input.

Applied value: 12

Follow the highlighted cells. Switch to Your turn to edit. Answer cells: E2, E3, E4, E5, E6. Browser calculations may differ from your Excel version.

Selection & formula search

Practice stays on this device. No worksheet data is uploaded.

Notes & examples
About this lesson
Discrete probability16 min·Growing

Build a complete binomial report for a fixed number of independent trials with one constant event probability.

THE QUICK ANSWER01

Build a complete binomial report for a fixed number of independent trials with one constant event probability.

E2=BINOM.DIST($B$4,$B$2,$B$3,FALSE)
E3=BINOM.DIST($B$4,$B$2,$B$3,TRUE)
E4=IF($B$7=0,1,IF($B$7>$B$2,0,SUM(BINOM.DIST(SEQUENCE($B$2-$B$7+1,1,$B$7),$B$2,$B$3,FALSE))))
E5=BINOM.DIST.RANGE($B$2,$B$3,$B$5,$B$6)
E6=$B$2*$B$3
For the example data
E2 0.2362232012800002E3 0.7945689497600003E4 0.44165425152000026E5 0.7057168138240002E6 2.4000000000000004

Enter each formula in its labeled answer cell. These report formulas perform different jobs; do not fill the first formula down.

UNDERSTAND THE IDEA

How it works

Read the event before choosing a function

Enter separate formulas in E2:E6. B2 is the fixed number of independent trials, B3 the same event probability in every trial and B4 an exact count. E2 is P(X=B4); E3 is P(X<=B4); E4 is P(X>=B7); E5 is P(B5<=X<=B6), including both endpoints; E6 is the expected count. Keep probabilities as unrounded proportions. Preserve small nonzero tails rather than rounding them to zero.

Keep the supplied model explicit

Use a whole n from 1–60, a numeric event proportion p from 0–1, whole k/a/b within 0–n with a<=b, and a whole threshold t from 0 through n+1. A proportion such as 0.2 means 20%; entering 20 defines no valid probability. Requested positive outputs must remain representable in the supported numeric precision.

Retain full computed precision

Probability outputs are proportions, not percentages entered as whole numbers. Grading compares nonzero values relatively, so a rare positive event cannot pass as numeric zero. Full-precision copies keep the actual formula and result. The fitted or assumed model is not a guarantee of real outcomes.

Read the full step-by-step walkthrough
  1. Declare the trial model

    There are n fixed independent trials. Each has one event/no-event result and the same supplied event probability. Sampling a changing finite population without replacement is a different model.

  2. Separate exactly from at most

    FALSE selects one count; TRUE includes every count from zero through k. These are different questions even when a boundary happens to make the answers equal.

  3. Include the upper-tail boundary

    At least t includes t. Sum its individual masses through n. Handle t=0 as one and t>n as zero before constructing the count sequence.

  4. Keep both interval endpoints

    BINOM.DIST.RANGE includes every whole count from a through b. If a equals b, the interval probability is one exact-count mass.

  5. Distinguish a count from a probability

    The expected count is n*p. It need not be a whole number, and it is not the chance that one specific count occurs.

WHEN SOMETHING LOOKS OFF

Things to watch

Using the cumulative flag for an exact count

TRUE includes earlier counts; use FALSE for P(X=k).

Dropping the threshold itself

P(X>=t) includes t. P(X>t) starts at t+1.

Replacing a rare event with zero

A small probability remains meaningful. Sum the tail directly when subtracting a cumulative result from one loses the remaining digits.

About this example

Original source models checked with real browser formulas and independent combinatorial/series targets. Native execution remains separate.

Browser: testedExcel: not verifiedGoogle Sheets: not verified

Content version 1. Practice checks compare calculated results across different datasets; they do not certify every possible formula.

Reference material