Probability of Events and Venn Diagrams

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, common mistakes in probability calculations, and the use of Venn diagrams to visualize intersections. Examples include calculating the probability of being blonde or female and owning a dog or cat.

What is the key characteristic of disjoint events?

• They always have the same probability.

• They can occur at the same time.

• They cannot occur at the same time.

• They are always mutually inclusive.

Which of the following is an example of non-disjoint events?

• Having blue eyes or brown hair

• Having green eyes or blue eyes

• Owning a car or a bicycle

• Being a teacher or a student

What common mistake do people make when calculating probabilities of non-disjoint events?

• Ignoring the probability of individual events

• Subtracting probabilities instead of adding

• Multiplying probabilities of all events

• Adding probabilities without considering intersection

What does the intersection of two events represent in a Venn diagram?

• The total probability of both events

• The probability of either event occurring

• The probability of both events occurring simultaneously

• The probability of neither event occurring

How do you adjust the addition rule for non-disjoint events?

• Divide the probability of one event by the other

• Subtract the probability of the intersection from the sum of individual probabilities

• Multiply the probabilities of both events

• Add the probabilities of both events

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

• 7 tenths

• 5 tenths

• 10 tenths

• 3 tenths

What is the probability of being blonde or female in the given example?

• 3 tenths

• 5 tenths

• 10 tenths

• 7 tenths

In the dog or cat ownership example, what is the probability of owning both?

• 0.39

• 0.57

• 0.46

• 0.28

What is the final probability of owning a dog or a cat?

• 0.39

• 0.28

• 0.46

• 0.57

Which rule is used to calculate the probability of non-disjoint events?

• Subtraction rule

• Division rule

• Addition rule

• Multiplication rule