Addition Rule and Venn Diagrams

Front

What is the Addition Rule in probability?

Back

The Addition Rule states that the probability of the occurrence of at least one of two events A or B is given by: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

How do you represent the probability of neither event A nor event B occurring?

Back

The probability of neither event A nor event B occurring is represented as P((A ∪ B)^c), which is equal to 1 - P(A ∪ B).

Front

What does a Venn diagram represent in probability?

Back

A Venn diagram visually represents the relationships between different sets, showing how they overlap and the probabilities of their unions and intersections.

Front

If 14 students are taking English Composition and 29 are taking Chemistry, how many are taking both if 5 students are in both classes?

Back

5 students are taking both classes.

Front

How do you calculate the number of students taking neither class if there are 40 students total?

Back

Number of students in neither class = Total students - (Students in English + Students in Chemistry - Students in both) = 40 - (14 + 29 - 5) = 2.

Front

What is the probability that a student does not take English Composition if 14 out of 40 students are taking it?

Back

The probability that a student does not take English Composition is P(not A) = 1 - P(A) = 1 - (14/40) = 26/40 = 13/20.

Front

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

Back

The formula for the probability of the intersection of two events A and B is P(A ∩ B) = P(A) + P(B) - P(A ∪ B).

Front

How do you find the probability of drawing a king or a club from a standard deck of cards?

Back

P(King or Club) = P(King) + P(Club) - P(King ∩ Club) = (4/52) + (13/52) - (1/52) = 16/52 = 4/13.

Front

What does P(A^c) represent in probability?

Back

P(A^c) represents the probability of the complement of event A, meaning the probability that event A does not occur.

Front

In a Venn diagram, what does the area outside both circles represent?

Back

The area outside both circles in a Venn diagram represents the outcomes that are not part of either event A or event B.