Conditional Probability and Events

This video tutorial by Simply Learn covers the fundamental concepts of conditional probability, starting with random experiments and sample space. It explains the multiplication rule for both independent and dependent events, providing examples for better understanding. The tutorial then delves into conditional probability, illustrating it with practical examples. The session concludes with a demonstration in Excel, reinforcing the concepts discussed.

What is a random experiment?

• An experiment with a known set of possible outcomes but unpredictable results

• An experiment that always yields the same result

• An experiment with an unknown set of outcomes

• An experiment with a predictable outcome

What is the sample space when a die is rolled?

• 1, 2, 3, 4

• 1, 2, 3, 4, 5, 6, 7

• 1, 2, 3, 4, 5

• 1, 2, 3, 4, 5, 6

How do you calculate the probability of two independent events occurring together?

• Add the probabilities of each event

• Multiply the probabilities of each event

• Divide the probability of one event by the other

• Subtract the probability of one event from the other

What is the probability of getting two heads when a coin is tossed twice?

• 0.5

• 0.25

• 0.75

• 1.0

What changes when two events are dependent?

• The sample space

• The probability of the second event

• The outcome of the first event

• The total number of outcomes

What is the probability of drawing a second card from a deck if the first card is not replaced?

• 1/49

• 1/50

• 1/51

• 1/52

How is conditional probability denoted?

• P(A and B)

• P(A or B)

• P(B|A)

• P(A|B)

If the probability of a student being a girl is 0.51 and the probability of a girl playing sports is 0.10, what is the conditional probability that a student plays sports given she is a girl?

• 0.51

• 0.10

• 0.05

• 0.1961

In the Excel example, what is the probability of a buyer purchasing football given they also purchased hockey?

• 0.4

• 0.5

• 0.2

• 0.7

What is the probability of purchasing both football and hockey in the Excel example?

• 0.5

• 0.4

• 0.2

• 0.7