Calculating the Probability of Non-Disjoint Events: Addition Rule

This lesson teaches how to calculate the probability of non-disjoint events using the addition rule. It explains the difference between disjoint and non-disjoint events, highlighting common mistakes in probability calculations. The lesson provides examples to illustrate the correct method, emphasizing the need to subtract the intersection probability when events are not disjoint.

What is the key characteristic of disjoint events?

• They can occur at the same time.

• They cannot occur at the same time.

• They are always mutually inclusive.

• They always have the same probability.

Which of the following is a common mistake when calculating probabilities for non-disjoint events?

• Ignoring the probability of the intersection.

• Adding the probabilities without considering intersections.

• Multiplying the probabilities of the events.

• Subtracting the probabilities of the events.

What symbol is used to represent the intersection of two events in probability?

• An upside-down U (∩)

• A division sign (÷)

• A minus sign (-)

• A plus sign (+)

How do you calculate the probability of non-disjoint events A or B?

• Add the probabilities of A and B.

• Multiply the probabilities of A and B.

• Add the probabilities of A and B, then subtract the probability of their intersection.

• Subtract the probabilities of A and B.

Why is it important to subtract the intersection probability when using the addition rule for non-disjoint events?

• To simplify the calculation.

• To ensure the total probability does not exceed 1.

• To avoid double-counting the intersection.

• To increase the total probability.

In the example of calculating the probability of being blonde or female, what is the probability of being both?

• 5/10

• 3/10

• 7/10

• 1/10

What is the probability of owning a dog or a cat, given the probabilities of owning a dog, a cat, and both?

• 0.28

• 0.57

• 0.39

• 0.46