Question

Suppose that $n$ independent trials, each of which results in any of the outcomes $0,1,$ or $2,$ with respective probabilities $p_{0}, p_{1},$ and $p_{2}, \sum_{i=0}^{2} p_{i}=1,$ are performed. Find the probability that outcomes 1 and 2 both occur at least once.

Name: Suppose that n independent trials, each of which results in any of the outcomes 0,1, or 2, with respective probabilities p0, p1, and p2, ∑i=0^2 pi=1, are performed. Find the probability that outcomes 1 and 2 both occur at least once.
Uploaded: 2023-02-10T23:27:02-08:00
Duration: 2 min 56 s
Channel: Lucas Finney
Description: Suppose that n independent trials, each of which results in any of the outcomes 0,1, or 2, with respective probabilities p0, p1, and p2, ∑i=0^2 pi=1, are performed. Find the probability that outcomes 1 and 2 both occur at least once.

          Suppose that $n$ independent trials, each of which results in any of the outcomes $0,1,$ or $2,$ with respective probabilities $p_{0}, p_{1},$ and $p_{2}, \sum_{i=0}^{2} p_{i}=1,$ are performed. Find the probability that outcomes 1 and 2 both occur at least once.

Added by Casey F.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Lucas Finney

02/10/2023

Step 1

This means that in all $n$ trials, we only get outcomes 0 or 2. The probability of this happening is $(p_0 + p_2)^n$. Similarly, we find the probability that outcome 2 does not occur at all. This means that in all $n$ trials, we only get outcomes 0 or 1. The Show more…

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Suppose that $n$ independent trials, each of which results in any of the outcomes $0,1,$ or $2,$ with respective probabilities $p_{0}, p_{1},$ and $p_{2}, \sum_{i=0}^{2} p_{i}=1,$ are performed. Find the probability that outcomes 1 and 2 both occur at least once.