Independent solution

How to solve this Poisson Distribution question

Setup

Setup

Express the requested probability as a conditional Poisson tail.

Pr⁡(X≥3∣X≥1)=Pr⁡(X≥3)Pr⁡(X≥1)\Pr(X\ge3\mid X\ge1)=\frac{\Pr(X\ge3)}{\Pr(X\ge1)}

Model

Model

Use complements to evaluate the numerator and denominator.

Pr⁡(X≥3)=1−e−1.2(1+1.2+1.222)\Pr(X\ge3)=1-e^{-1.2}\left(1+1.2+\frac{1.2^2}{2}\right)
Pr⁡(X≥1)=1−e−1.2\Pr(X\ge1)=1-e^{-1.2}

Compute

Compute

Divide the unconditional upper tail by the probability of a positive count.

Pr⁡(X≥3)=0.1205129012\Pr(X\ge3)=0.1205129012
Pr⁡(X≥1)=0.6988057881\Pr(X\ge1)=0.6988057881
Pr⁡(X≥3∣X≥1)=0.1724554995\Pr(X\ge3\mid X\ge1)=0.1724554995

Answer

Answer

The conditional probability rounds to 0.17.

0.17(D)\boxed{0.17\quad\text{(D)}}