Type the R transcript that prints the pmf at 2, the cumulative probability up to 2, and the upper tail from 3 for Bin(12, 0.15).
Type the R transcript that prints the pmf at 2, the cumulative probability up to 2, and the upper tail from 3 for Bin(12, 0.15).
Answer
> dbinom(2, 12, 0.15) [1] 0.2923585 > pbinom(2, 12, 0.15) [1] 0.7358181 > 1 - pbinom(2, 12, 0.15) [1] 0.2641819
dbinom is P(X = x); pbinom is P(X ≤ k); 1 − pbinom(2, …) is P(X ≥ 3). The three lines are the hand values 0.2924, 0.7358 and 0.2642 at seven significant figures.
IBS1 §4.2 (cumulative binomial probabilities), CC BY 4.0 — shape only; R documentation for dbinom/pbinom; every R line is the verbatim console text of a real Rscript run (2026-09-17); original dataset