Calculating Binomial Probabilities (Edexcel A-Level Mathematics): Flashcards

Running total of probability, or $P(X \leq n)$.

Binomial distribution with $n=20$, $p=0.3$.

Use Binomial CD: Enter $X=10$, $N=20$, $p=0.3$.

$P(X \leq 10) = 0.9829$.

$P(X > 6) = 1 - P(X \leq 6)$.

$P(X > 6)$ can be calculated using cumulative distribution.

Use Binomial PD: $X=5$, $N=20$, $p=0.35$.

Use $P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{(n-k)}$.

$P(2 ≤ X ≤ 7) = P(X ≤ 7) - P(X ≤ 1)$.

$P(2 ≤ X ≤ 7) = 0.5989$.