5.05 Conditional probability

Lesson

Practice

Adaptive

Worksheet

Interactive practice questions

A basketball team has a probability of $0.8$0.8 of winning its first season and $0.15$0.15 of winning its first season and its second season. What is the probability of winning the second season, given they won first?

Give your answer in its simplest form.

Medium

3min

Medium

1min

For events $A$A and $B$B we can find the probability of $A$A given $B$B using$P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$P(A|B)=P(A∩B)P(B).

Medium

1min

The following are probabilities for an experiment in which $A$A and $B$B are two possible events.

$P\left(A\cap B\right)=0.48$P(A∩B)=0.48, and

$P\left(A\right)=0.6$P(A)=0.6.

Find $P\left(B|A\right)$P(B|A).

Medium

1min

Outcomes

S.CP.A.3

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S.CP.A.4

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

S.CP.A.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

S.CP.B.6

Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

S.CP.B.8 (+)

Apply the general multiplication rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

S.MD.B.6 (+)

Use probabilities to make fair decisions.

5.05 Conditional probability

Interactive practice questions

Outcomes

S.CP.A.3

S.CP.A.4

S.CP.A.5

S.CP.B.6

S.CP.B.8 (+)

S.MD.B.6 (+)

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