Conditional Independence

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

How many people chose neither?

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)

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

P(A|B)=

Are the events "blonde" hair and "blue" eyes independent?

• Independent because P(blonde) = P(blonde | blue)

• Not Independent P(blonde) ≠ P(blonde | blue)

• Independent because P(blonde) = P(blue)

• Not Independent P(blonde) ≠ P(blue)

P(Pizza|Senior):

• 10/15

• 4/5

• 2/3

• 10/5

Let M represent the event of randomly selecting a male. Let S represent the event of randomly selecting a person that drives a SUV.

Determine if the events M and S are independent.

• Independent

• Not Independent

Are the events "first class passenger" and "survived" independent?

• Independent P(first class) = P(first class | survived)

• Not Independent P(first class) ≠ P(first class | survived)

• Independent P(first class) = P(not first class)

• Not Independent P(first class) ≠ P(first class and survived)

What is P(T given C)?

• 45%

• 29.6%

• 40%

• 33.3%