Complementary Probability Concepts

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 real-world example involving favorite sports to demonstrate how to apply probability equations. The video concludes with a summary and suggests further resources for learning.

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

• Rolling a 3 through 6

• Rolling an even number

• Rolling a 1 or 2

• Rolling a 6

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

• 0.75

• 0.25

• 1

• 0.5

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

• Probability of event E

• Probability of neither E nor E prime

• Probability of both E and E prime

• Probability of E prime

If the probability of event E is 0.35, what is the probability of E prime?

• 0.15

• 0.65

• 0.50

• 0.35

How can you calculate the probability of E using E prime?

• Subtract the probability of E prime from 1

• Divide the probability of E prime by 2

• Multiply the probability of E prime by 2

• Add the probability of E prime to 1

In a survey of 50 people, how many said football was their favorite sport?

• 11

• 29

• 6

• 3

What is the probability that a randomly selected person does not prefer football?

• 0.29

• 0.42

• 0.58

• 0.71

Which equation is used to find the probability of E prime?

• P(E) + P(E') = 1

• P(E') = 1 - P(E)

• P(E) = 1 + P(E')

• P(E) = P(E') - 1

If 21 out of 50 people do not prefer football, what is the probability in percentage?

• 58%

• 42%

• 21%

• 50%

What is the main use of complementary probability in real-world scenarios?

• To increase the probability of an event

• To determine the exact outcome of an event

• To calculate the likelihood of an event not happening

• To predict future events