5-2 Concept Check

Front

What does A∩B represent in set theory?

Back

A∩B represents the intersection of sets A and B, which includes all elements that are common to both sets.

Front

What does A∪B represent in set theory?

Back

A∪B represents the union of sets A and B, which includes all elements that are in either set A, set B, or both.

Front

What is the complement of an event A, denoted as A^C?

Back

The complement of an event A, denoted as A^C, includes all outcomes in the sample space that are not in A.

Front

If P(A) = 0.12, what is P(A^C)?

Back

P(A^C) = 1 - P(A) = 1 - 0.12 = 0.88.

Front

What is a valid probability model?

Back

A valid probability model must satisfy two conditions: all probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.

Front

What does the notation P(Football ∪ Wrestle) represent?

Back

P(Football ∪ Wrestle) represents the probability that a student plays either football or wrestles or both.

Front

What is the formula for finding the probability of the union of two events A and B?

Back

The formula is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

What does A^C ∩ B^C represent?

Back

A^C ∩ B^C represents the intersection of the complements of sets A and B, which includes all elements that are in neither A nor B.

Front

How do you calculate the probability of the intersection of two independent events A and B?

Back

For independent events, P(A ∩ B) = P(A) * P(B).

Front

What is the difference between mutually exclusive and independent events?

Back

Mutually exclusive events cannot occur at the same time, while independent events do not affect each other's probabilities.