Binomial distribution: P(X = k)
P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ. Forget the binomial coefficient and you count only one order.
Worked example
A multiple-choice question is guessed correctly with probability 0.10. 10 questions are guessed. What is P(exactly 3 correct)?
Worked solution
- 1.X ~ B(n = 10; p = 0.10)
- 2.P(X = 3) = (10 über 3) · 0.10^3 · 0.90^7
- 3.= 120 · 0.001000 · 0.478297 = 0.0574
Typical mistake: Forgetting the binomial coefficient.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task 1 of 3Binomial distribution
Task
A multiple-choice question is guessed correctly with probability 0.50. 6 questions are guessed. What is P(exactly 2 correct)?
P(X = 2) (4 decimal places)
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ
- P(X ≤ k) = P(X = 0) + … + P(X = k)
- E(X) = n · p, σ = √(n · p · (1 − p))
Typical mistake: Forgetting the binomial coefficient.
Frequently asked questions
What is the typical mistake in "Binomial distribution: P(X = k)"?
Forgetting the binomial coefficient.
How do I work out "at least k"?
Use the complement: P(X ≥ k) = 1 − P(X ≤ k − 1).