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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.

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Answer:

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

Step-by-step 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 [tex]\frac{20}{40}=0.5[/tex]
  2. the probability that the card shows diamond is [tex]\frac{10}{40}=0.25[/tex]
  3. finally the probability that the card is black or shows a diamond is 0.5 + 0.25 = 0.75