Binomial Probability
Statistics
Intro: We compute exact $P(X=k)$ for $X \sim \mathrm{Bin}(n,p)$.
Worked example
- n=10, p=0.3, k=4
- Goal: For $X\sim\mathrm{Bin}(n,p)$ compute $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$.
- Inputs: $n=10,\; p=0.3,\; k=4\Rightarrow 1-p=0.7$.
- Coefficient: $\binom{10}{4}=\dfrac{10!}{4!6!}=210$.
- Powers: $0.3^4=0.0081$, $0.7^6\approx0.117649$.
- Multiply: $P=210\times0.0081\times0.117649\approx0.2000$.
- Answer: $\boxed{P(X=4)\approx0.200}$.
FAQs
Cumulative P(X≤k)?
Sum from 0 to k of the pmf; we can display cumulative as well.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.