Per 3 Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event 'A' occurring given that another event 'B' has occurred, denoted as P(A|B).

Front

How is Conditional Probability calculated?

Back

P(A|B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events occurring.

Front

What does P(A|B) represent?

Back

The probability of event A occurring given that event B has occurred.

Front

If P(A) = 0.5 and P(B) = 0.4, what is P(A|B) if P(A and B) = 0.2?

Back

P(A|B) = P(A and B) / P(B) = 0.2 / 0.4 = 0.5.

Front

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

Back

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

Front

What is the probability that a student takes Spanish given that they take Technology?

Back

P(Spanish|Technology) = P(Spanish and Technology) / P(Technology).

Front

What is the probability of event A occurring when event B has occurred called?

Back

Conditional probability of event A.

Front

If the probability of rain on Monday is 4/5 and on Tuesday is 2/3, what is the probability it will rain both days?

Back

P(Rain Monday and Tuesday) = P(Rain Monday) * P(Rain Tuesday) = (4/5) * (2/3) = 8/15.

Front

What is the probability of drawing an Ace from a deck of cards given that the card is a heart?

Back

P(Ace|Hearts) = 1/13 = 7.7%.

Front

What is the relationship between joint probability and conditional probability?

Back

Joint probability P(A and B) can be expressed as P(A|B) * P(B).