Mathematik — Stochastik (Statistics & Probability) for the Abitur Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Confusing "with replacement" and "without replacement" in probability calculations
• !Incorrect binomial coefficient calculation: n over k (n!/(k!(n-k)!))
• !Not correctly formulating the null hypothesis for significance tests

Study tips

• 1Memorize the binomial probability formula: P(X = k) = C(n,k) × p^k × (1-p)^(n-k).
• 2Practice cumulative binomial probability tables — many Abitur questions ask for P(X ≤ k) or P(X ≥ k).
• 3For hypothesis tests, follow the standard steps: H₀ and H₁ formulation → significance level → critical region → decision.

Sample Abitur Mathematik — Stochastik (Statistics & Probability) questions

These sample items mirror the format and difficulty of real Abitur questions. Practice with thousands more on the free Koydo question bank.

1. 1

   Ein fairer Würfel wird 6-mal geworfen. Mit welcher Formel berechnet man P(genau 2-mal eine 6)? (A fair die is rolled 6 times. Which formula gives P(exactly 2 sixes)?)

   • AP = C(6,2) × (1/6)² × (5/6)⁴Correct
   • BP = 2 × (1/6) × (5/6)
   • CP = (1/6)² × (5/6)⁴
   • DP = C(6,2) × (1/6)⁶
   Why this answer?

   The binomial formula is B(n,k,p): P(X=k) = C(n,k) × p^k × (1-p)^(n-k). Here n=6, k=2, p=1/6: P = C(6,2) × (1/6)² × (5/6)⁴. C(6,2) = 15; (1/6)² = 1/36; (5/6)⁴ = 625/1296.