5.3.3 - Disjoint / Independence

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?

• Independent
• Dependent

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

CCSS.HSS.CP.B.8

What does it mean for two events to be independent of each other?

• What happens in the second event depends on what happens in the first.

• The result of the first event has no effect on the result of the next event.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.4

CCSS.HSS.CP.B.8

Clara picks a marble at random, puts it back, and then picks another marble at random.

• Dependent
• Independent

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

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

If A and B are mutually exclusive, which statement below must be true?

• P(A∩B) = 0

• P(A|B) = 0

• P(A∪B) = 0

• P(A) + P(B) = 1

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.7

If you are picking a card randomly from a deck of cards, the events of picking an ace and picking a ‘3’ are mutually exclusive.

• True

• False

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.7

Given the probabilities P(A) =0.4 and P(A∪B) =0.6, what is the probability P(B): If A and B are mutually exclusive? If A and B are independent? 

• a) 0.2; 0.4
• b) 0.2; 0.33
• c) 0.33; 0.2
• d) 0.6; 0.33

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.B.7

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

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

• Independent

• Not Independent

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

• Independent

• Not Independent