Independent solution

How to solve this Binomial and Multinomial Distributions question

Answer in brief

Each of the two independent outcomes avoids the target category with probability 0.9. Therefore, the probability that the target occurs at least once is 1 - 0.9^2 = 0.19, so the answer is D.

Setup

Setup

For one outcome, the target category has probability 0.1, so its complement has probability 0.9.

P(not target)=1−0.1=0.9P(\text{not target})=1-0.1=0.9

Model

Model

Use independence to calculate the probability that neither of the two outcomes falls in the target category.

P(no target in two outcomes)=(0.9)2P(\text{no target in two outcomes})=(0.9)^2

Compute

Compute

Take the complement of the event that the target never occurs.

P(at least one target)=1−(0.9)2=0.19P(\text{at least one target})=1-(0.9)^2=0.19

Answer

Answer

The required probability is 0.19.

0.19(D)\boxed{0.19\quad\text{(D)}}