Question

Which of the following choices can be considered binomial random variables?

(Choice A) A container holds 20 pens, half of which are red. Select an SRS of 5 pens and let Q = the number of red pens obtained.

(Choice B) A container holds 1000 pens, half of which are red. Select an SRS of 5 pens and let S = the number of red pens obtained.

(Choice C) A container holds 100100100 pens, half of which are red. Select an SRS of 5 pens and let R = the number of red pens obtained.

A. Choice A only
B. Choices A and B
C. Choices A and C
D. Choices B and C

Answer 1

Choices A and B can be considered binomial random variables because they meet the conditions of a binomial distribution.

Step-by-step explanation:

The binomial random variables are the ones that satisfy the conditions of a binomial distribution:

1. There are a fixed number of independent trials.
2. Each trial has two possible outcomes, success or failure.
3. The probability of success remains the same for each trial.

In this case, choice A and choice B can be considered binomial random variables because they meet these conditions. Choice A involves selecting red pens from a container containing 20 pens, half of which are red. Choice B involves selecting red pens from a container containing 1000 pens, half of which are red.