This video tutorial discusses conditional probability through classic boy-girl problems. It covers two scenarios: the probability of both children being boys given at least one is a boy, and the probability of both being boys given the older child is a boy. The tutorial explains the sample set, intersection, and probability calculations, providing a clear understanding of these concepts. Additional resources and links to related videos are also provided.

What is the main topic discussed in this tutorial?

• Conditional probability

• Linear regression

• Descriptive statistics

• Bayesian inference

In the first problem, what is the probability that both children are boys given that at least one is a boy?

• 1/2

• 1/4

• 1/3

• 1/5

Which of the following is NOT a possible combination of children in the first problem?

• Boy and Boy

• Boy and Girl

• Girl and Girl

• Girl and Boy

What is the sample space for the first problem after eliminating the impossible combination?

• Boy and Boy, Boy and Girl

• Boy and Girl, Girl and Girl

• Boy and Girl, Boy and Boy, Girl and Boy

• Boy and Boy, Girl and Girl

In probability notation, what does P(A|B) represent?

• Probability of A given B

• Probability of B given A

• Probability of A and B

• Probability of A or B

What is the denominator in the probability calculation for the first problem?

• 2

• 3

• 5

• 4

In the second problem, what condition is given about the children?

• The younger child is a girl

• Both children are girls

• At least one child is a boy

• The older child is a boy

How many cases are there where the older child is a boy in the second problem?

• 1

• 2

• 3

• 4

What is the probability that both children are boys given the older child is a boy?

• 1/4

• 1/3

• 1/2

• 1/5

What is the numerator in the probability calculation for the second problem?

• 4

• 1

• 2

• 3