Determining Independence with Conditional Probability

The video tutorial explains how to determine if events are independent using conditional probability. It reviews the definition of independent events and provides examples using class data to illustrate the concept. The tutorial emphasizes that events A and B are independent if the probability of A given B equals the probability of A, and vice versa. Examples include analyzing the independence of wearing jeans and being female or male, and wearing sneakers and being male. The video clarifies common misconceptions about event independence.

What is the condition for two events A and B to be considered independent?

• The probability of A given B is greater than the probability of B.

• The probability of A is equal to the probability of B.

• The probability of A and B is equal to the product of their individual probabilities.

• The probability of A given B is less than the probability of A.

In Shaela's class, what is the probability of a student being female and wearing jeans?

• 12 out of 21

• 6 out of 21

• 14 out of 21

• 8 out of 21

How do you determine if wearing jeans and being female are independent events in Shaela's class?

• By checking if the probability of wearing jeans is equal to the probability of being female.

• By checking if the probability of wearing jeans given female is equal to the probability of wearing jeans.

• By checking if the probability of being female given wearing jeans is equal to the probability of being female.

• By checking if the probability of wearing jeans and being female is greater than the probability of wearing jeans.

What conclusion can be drawn if the conditional probability of A given B is the same as the probability of A?

• Events A and B are dependent.

• Event B is more likely than event A.

• Event A is more likely than event B.

• Events A and B are independent.

What is a common misconception about the independence of events A and B?

• That the probability of A given B is the same as the probability of A.

• That the probability of A given B is the same as the probability of B.

• That the probability of A and B is less than the probability of A.

• That the probability of A and B is greater than the probability of B.

In Bailey's class, what is the probability of being male if a student wears sneakers?

• 8 out of 16

• 9 out of 21

• 12 out of 26

• 6 out of 14

What does it mean if two fractions representing probabilities are not equal in a given scenario?

• The events are equally likely.

• The events are mutually exclusive.

• The events are dependent.

• The events are independent.