Question

A video game randomly chooses the colors of your character’s shirt and pants. The probability that you get a blue shirt is 0.18. The probability that you get a blue shirt given that you get blue pants is 0.18. Are the colors of your character’s shirt and pants independent events? Why or why not?

Answer 1

The events are independent;

Since P(A) = P(A|B).

Where:

A is the outcome of picking a blue shirt

B is the outcome of picking blue pants

Explanation:

Independent events are ones which can both occur but do not affect the probability of each other occurring;

In this case, whether or not blue pants are picked is irrelevant, the probability of a blue shirt is 0.18, i.e. it doesn't change, therefore the events are independent.