Question

What is the probability that a person's favorite vehicle color is black or silver? If the favorite is black, it cannot be silver, so these two events are disjoint. Using Rule 3?

Answer 1

The probability that a person's favorite vehicle color is black or silver is 0.50.

Explanation:

The color options are: Black and Silver.

The probability that a person's favorite vehicle color is black or silver is same, i.e.

`P(Black)=P(Silver)=(1)/(2)`

Also it is provided that if a person's favorite color is black then it cannot be silver and vice versa.

This implies that the event that a person's favorite color is black and the event that person's favorite color is silver are mutually exclusive or disjoint event.

Mutually exclusive or disjoint events are those events that cannot occur together. That is, if A and B are disjoint then P (A and B) = 0.

Compute the probability of the events of a person liking black or silver as follows:

`P(Black\cup Silver)=P(Black)+P(Silver)-P(Black\cap Silver)\\=(1)/(2)+(1)/(2)-0\\ =(1)/(2)`

Thus, the probability that a person's favorite vehicle color is black or silver is 0.50.