Conditional Probability And Independence

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Conditional Probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does it mean for two events to be independent?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, P(A|B) = P(A) and P(B|A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

How do you calculate the probability of two independent events both occurring?

Back

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

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the Total Probability Theorem?

Back

If B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

What is the Law of Total Probability?

Back

It states that the total probability of an event can be found by considering all the different ways that event can occur, weighted by the probabilities of those ways.

Front

What is the difference between theoretical probability and experimental probability?

Back

Theoretical probability is based on the possible outcomes in a perfect world, while experimental probability is based on actual experiments and observed outcomes.

Front

How do you find the probability of drawing a specific color marble from a bag?

Back

Divide the number of favorable outcomes (specific color marbles) by the total number of outcomes (total marbles in the bag).

Tags

CCSS.7.SP.C.7B

Front

What is the probability of drawing two marbles of the same color without replacement?

Back

P(same color) = (number of first color marbles / total marbles) * (number of remaining same color marbles / remaining total marbles).

Front

What is the probability of flipping a coin and then spinning a spinner?

Back

Multiply the probability of each independent event: P(Heads) * P(Yellow). For a fair coin and a spinner with equal sections, P(Heads) = 1/2 and P(Yellow) = 1/n (where n is the number of sections).