Conditional Probability & Independence

Are the events "Sports" and "Community Service" independent?

• Yes, because P(S) is the same as P(S|CS).

• No, because P(S) is not the same as P(S|CS).

• Yes, because P(S) is the same as P(CS|S).

• No, because P(S) is not the same as P(CS|S).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.4

CCSS.HSS.CP.B.6

Are the events "takes Spanish" and "participates in a club" independent events?

• Yes, because P(S) is the same as P(S|C).

• No, because P(S) is not the same as P(S|C).

• Yes, because P(S) is the same as P(C|S).

• No, because P(S) is not the same P(C|S).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.4

CCSS.HSS.CP.B.6

CCSS.HSS.CP.B.8

Determine if the events A and B are independent or dependent. P(A) = .36, P(B) = .20, P (A and B) = 0.072

• Dependent

• Independent

• Neither

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.8

Find P(Sophomore U Pass)

• 53/60

• 70/60

• 5/6

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.9

If A and B are independent, which statement must be true?

• P(A∩B) = 0

• P(A|B) = P(A)

• P(A∪B) = 0

• P(A) + P(B) = 1

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.4

CCSS.HSS.CP.B.8

P(A)=2/5 P(B)=1/5 P(A and B)=2/25

• Dependent

• Independent

Are the events A and B independent. Select a response and a reason.

• Yes

• No

• because P(A) = P(A|B)

• because P(A) ≠ P(A|B)

If in a random survey of 40 people,17 select option A, 24 select option B, and 13 select option B only, then...

Are choices A and B independent?

• Yes

• No

• because P(A) = P(A|B)

• because P(A) ≠ P(A|B)

P(A) = 0.79 and P(B) = 0.39 and they are independent events.

Find P(A and B).

RECALL: P(A and B) = P(A) * P(B|A)

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the given table. You want to determine whether gender and passing the test are independent. Select the correct independence calculation.

• P(Female) = 153/221; P(Female | Passed) = 117/169

• P(Female) = 153/221; P(Female | Passed) = 117/153

• P(Female) = 153/221; P(Passed | Female) = 117/153

• P(Female) = 153/221; P(Passed | Female) = 117/169