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 Probability.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Front

What does P(A | B) represent?

Back

P(A | B) represents the conditional probability of event A occurring given that event B has occurred.

Front

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

Back

P(A and B) = P(A) * P(B) for independent events.

Front

What is the formula for conditional probability?

Back

P(A | B) = P(A and B) / P(B) where P(B) > 0.

Front

What does 'mutually exclusive' mean in probability?

Back

Mutually exclusive events cannot occur at the same time; the occurrence of one event excludes the possibility of the other.

Front

How do you find the probability of the union of two events A and B?

Back

P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the complement of an event A?

Back

The complement of event A, denoted as A', is the event that A does not occur.

Front

If 30% of students play football and 20% play basketball, what is the probability that a student plays either sport if 10% play both?

Back

P(Football or Basketball) = P(Football) + P(Basketball) - P(Both) = 0.30 + 0.20 - 0.10 = 0.40.

Front

What is the probability of selecting a boy given that the person speaks German?

Back

This is a conditional probability problem, calculated as P(Boy | German) = P(Boy and German) / P(German).