Probability and Its Complements

The video tutorial explains the concept of complementary events in probability, using examples like rolling a die. It introduces the notation for events and their complements, and discusses rules and equations related to complementary events. The tutorial uses Venn diagrams to visually represent these concepts and provides a practical example involving favorite sports to demonstrate how to calculate probabilities. The video concludes with a summary and suggestions for further learning.

What is the complement of the event of rolling a 1 or a 2 on a die?

• Rolling a 1 or a 2

• Rolling a 3 through 6

• Rolling a 2 through 4

• Rolling a 5 or a 6

If the probability of event E is 0.4, what is the probability of its complement E'?

• 1.0

• 0.6

• 0.4

• 0.2

Which equation represents the relationship between the probability of an event and its complement?

• P(E) * P(E') = 1

• P(E) - P(E') = 1

• P(E) + P(E') = 1

• P(E) + P(E') = 0

If the probability of E is 0.7, what is the probability of E'?

• 0.3

• 0.7

• 0.5

• 1.0

What is the total probability of all outcomes in a sample space?

• 0.75

• 1.0

• 0.25

• 0.5

In a Venn diagram representing probabilities, what does the area outside the circle represent?

• Total probability

• Probability of E'

• Probability of event E

• Probability of both E and E'

How can you calculate the probability of E if you know the probability of E'?

• Divide the probability of E' by 2

• Add the probability of E' to 1

• Multiply the probability of E' by 2

• Subtract the probability of E' from 1

In a survey of 50 people, 29 said football is their favorite sport. What is the probability that a randomly selected person does not prefer football?

• 0.58

• 0.71

• 0.42

• 0.29

If 11 people prefer basketball, what is the probability that a randomly selected person prefers basketball?

• 0.22

• 0.11

• 0.44

• 0.33

What is the probability of selecting someone whose favorite sport is tennis?

• 0.05

• 0.20

• 0.10

• 0.02