Maths · Probability: Probability of an event, addition and multiplication theorems of probability
If \propto k \) for the \) equals
If \( P\left(E_{k}\right) \propto k \) for \( 0 \leq k \leq n, \) the \( P(A) \) equals
- A. \( 3 n /(4 n+1) \)
- B. \( (2 n+1) / 3 n \)
- C. \( 1 /(n+1) \)
- D. \( 1 / n^{2} \)
Step-by-step solution
The probabilities sum to 1, so sum_{k=0}^n ck = 1, giving c = 2/(n(n+1)). Then P(E_k) = 2k/(n(n+1)). Assuming A is the event that a randomly chosen index (uniform from 0 to n) yields an event that occurs, the probability is (1/(n+1)) * sum P(E_k) = 1/(n+1).
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