Exploring Conditional Probability and Independence in AP Statistics

What does it mean for two events to be independent in probability?

• The occurrence of one event does not affect the probability of the other.

• The events have no outcomes in common.

• The outcome of one event affects the outcome of the other.

• Both events must occur simultaneously.

If you toss two coins, what is the probability of getting one head and one tail?

• 0.75

• 0.5

• 1

• 0.25

If the probability of an event A given B is equal to the probability of A, what can be inferred about events A and B?

• They are independent

• They are mutually exclusive

• They are dependent

• They are complementary

Can two mutually exclusive events be independent?

• Yes, always

• It depends on the event probabilities

• No, never

• Yes, but only under certain conditions

In the context of internet providers, if knowing a person uses Cox makes it impossible they use CenturyLink, what does this imply about the events?

• They are independent

• They are dependent

• They are overlapping

• They are mutually exclusive

What is the probability of a page having neither a data display nor equations?

• 41%

• 32%

• 20%

• 48%

What is the probability that a page with an equation also has a data display, given the provided data?

• 25.9%

• 48%

• 32%

• 7%

Are the events 'having an equation' and 'having a data display' on a page mutually exclusive?

• Only if there is no data display

• Yes

• No

• Cannot be determined

What does it imply if the probability of having a data display given an equation is not equal to the probability of just having a data display?

• The events are dependent

• The data is insufficient to conclude

• The events are independent

• The events are mutually exclusive

What is the probability of a page having an equation given it has a data display?

• 14.6%

• 25.9%

• 7%

• 48%