Probability #2 (Venn Diagrams, Conditional)

Front

What is a Venn Diagram?

Back

A Venn Diagram is a visual representation of the relationships between different sets, often used to illustrate the overlap between them.

Front

Define Conditional Probability.

Back

Conditional Probability is the probability of an event occurring given that another event has already occurred.

Front

What does it mean if two events are independent?

Back

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Front

How do you calculate the probability of the union of two events?

Back

P(A or B) = P(A) + P(B) - P(A and B) where A and B are two events.

Front

What is the formula for conditional probability?

Back

P(A|B) = P(A and B) / P(B) where P(A|B) is the probability of A given B.

Front

If 60% of students play football and 30% play basketball, what is the probability that a student plays either sport?

Back

If there is no overlap, P(Football or Basketball) = P(Football) + P(Basketball) = 0.60 + 0.30 = 0.90.

Front

What is the complement of an event?

Back

The complement of an event A is the event that A does not occur, denoted as A'. The probability of the complement is P(A') = 1 - P(A).

Front

How do you find the probability of an event not occurring?

Back

P(not A) = 1 - P(A).

Front

What is the intersection of two sets in a Venn Diagram?

Back

The intersection of two sets A and B, denoted as A ∩ B, is the set of elements that are common to both A and B.

Front

If 40% of students are girls and 25% of girls play soccer, what is the probability that a randomly selected student is a girl who plays soccer?

Back

P(Girl and Soccer) = P(Girl) * P(Soccer|Girl) = 0.40 * 0.25 = 0.10.