Conditional Probability and Sample Space

The video tutorial introduces the concept of conditional probability using various examples, such as rolling a die, family scenarios, and classroom settings. It explains the importance of sample space and subsets, and demonstrates how to calculate conditional probabilities. The tutorial emphasizes the significance of order in conditional probability expressions and provides practical examples to illustrate these concepts.

What is the probability that a die roll is even, given that the result is less than four?

• 1/2

• 1/3

• 1/4

• 1/6

What is the sample space for a six-sided die?

• 2, 4, 6

• 1, 2, 3, 4, 5, 6

• 1, 3, 5

• 1, 2, 3, 4, 5

How many outcomes are there in the subset of even numbers for a six-sided die?

• 5

• 4

• 3

• 2

What is the probability that a die roll is less than four?

• 1/2

• 2/3

• 1/3

• 1/4

If a family has two children and one is a daughter, what is the probability that the other child is a son?

• 3/4

• 2/3

• 1/2

• 1/4

Which of the following is true about the order in conditional probability expressions?

• P(A|B) is always greater than P(B|A)

• The order does not matter

• P(A|B) is usually different from P(B|A)

• P(B|A) is always equal to P(A|B)

In a spinner with outcomes 1 through 8 for event A and 6 through 10 for event B, what is P(B|A)?

• 3/8

• 3/5

• 5/8

• 1/2

If event A is outcomes 1 through 8 and event B is outcomes 6 through 10, what is P(A|B)?

• 1/2

• 5/8

• 3/5

• 3/8

What is the probability that a student wearing sneakers is male, given there are 16 students wearing sneakers and 8 are male?

• 3/4

• 1/2

• 2/3

• 1/3

In the classroom example, what is the probability of wearing sneakers given someone is male?

• 3/4

• 2/3

• 1/2

• 2/5