Question

Example 1: Use of the Addition Rule for Disjoint Events

A set of 40 cards consists of the following:
 10 black cards showing squares
 10 black cards showing circles
 10 red cards showing X’s
 10 red cards showing diamonds
A card will be selected at random from the set. Find the probability that the card is black or shows a diamond.

Answer 1

The probability that the card is black or shows a diamond is 0.75

Explanation:

The probability that the card is black or shows a diamond requires calculating the probabilities separately and adding them.

This is an example of Addition Rule for Disjoint Events

1. the probability that the card is black is
   `(20)/(40)=0.5`
2. the probability that the card shows diamond is
   `(10)/(40)=0.25`
3. finally the probability that the card is black or shows a diamond is 0.5 + 0.25 = 0.75