Complements and Conditional Probability

Front

What is the definition of probability?

Back

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

Tags

CCSS.7.SP.C.5

Front

What is a complement in probability?

Back

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

Tags

CCSS.HSS.CP.A.1

Front

How do you calculate the probability of an event?

Back

The probability of an event A is calculated as P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}.

Tags

CCSS.7.SP.C.7A

Front

What is conditional probability?

Back

Conditional probability is the probability of an event A given that event B has occurred, denoted as P(A|B) = \frac{P(A \cap B)}{P(B)}.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for finding the probability of at least one event occurring?

Back

The probability of at least one event occurring is given by P(at least one) = 1 - P(none).

Front

If 5% of light bulbs are defective, what is the probability that a randomly selected bulb is not defective?

Back

The probability that a randomly selected bulb is not defective is 95%, or P(not defective) = 0.95.

Tags

CCSS.HSS.CP.B.7

Front

How do you find the probability of two independent events occurring?

Back

For two independent events A and B, the probability of both A and B occurring is P(A \cap B) = P(A) \times P(B).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the probability of selecting a student not in a club from a sample of 378 students with 138 not in a club?

Back

P(not in club) = \frac{138}{378}.

Tags

CCSS.7.SP.C.7B

Front

What is the probability of selecting a student who takes Latin given they are in a club?

Back

P(Latin | in club) = \frac{41}{240}.

Tags

CCSS.HSS.CP.B.6

Front

What is the total probability rule?

Back

The total probability rule states that if events B1, B2, ..., Bn form a partition of the sample space, then P(A) = \sum_{i=1}^{n} P(A | B_i) P(B_i).