Calculating Conditional Probabilities

The video tutorial explains conditional probability, which is the probability of an event B occurring given that event A has already occurred. It introduces the formal equation for conditional probability and provides examples to illustrate the concept. The examples include rolling a die, smoking and lung cancer, and drawing cards from a deck. Each example demonstrates how to apply the conditional probability formula to calculate the probability of an event given a certain condition.

What does the notation P(B|A) represent in conditional probability?

• Probability of event A given event B

• Probability of event B given event A

• Probability of both events A and B

• Probability of event A or event B

Which of the following is the correct formula for conditional probability?

• P(B|A) = P(B) / P(A)

• P(B|A) = P(A and B) / P(A)

• P(A|B) = P(A) / P(B)

• P(A|B) = P(A and B) / P(B)

In the die example, what is the probability of rolling a 4 given that the number is even?

• 1/2

• 1/4

• 1/3

• 1/6

If the probability of being a smoker is 0.19 and the probability of being a smoker and developing lung cancer is 0.03, what is the probability of developing lung cancer given that you smoke?

• 0.19

• 0.25

• 0.158

• 0.03

What is the probability of drawing a second Jack from a deck, given that the first card drawn was a Jack?

• 1/52

• 1/13

• 3/51

• 4/52

How many Jacks are there in a standard deck of cards?

• 4

• 3

• 2

• 5

What is the probability of drawing two Jacks consecutively without replacement from a standard deck?

• 1/221

• 12/2652

• 1/52

• 1/13