I draw one card from a standard deck of cards and we define the events as follows EventA= card is a heart eventB= card is a diamond eventC= card is a face card

 

a) Are events A and B independent, dependent or mutually exclusive? Why or why not?

 

b) Are events A and C independent, dependent or mutually exclusive? Why or why not?

 

c) Are events B and C independent, dependent or mutually exclusive? Why or why not

 

d) Give an example of any Event D that is mutually exclusive of event B

a) Mutually Exclusive events, because a card cannot be both a heart and a diamond.

b) Independent Events, because P(A∩B)=P(A)·P(B) (test for independent events holds true.

c) Independent Events, because P(A∩B)=P(A)·P(B) (test for independent events holds true.

d) Event D = card is a spade

Step-by-step explanation

Independent events are events that have no effect on the probability of each other happening or not happening. P(A∩B)=P(A)·P(B) must also hold true or  which means the probability of both events happening is equal to the product of both events.

Dependent events are when the outcome of the first event affect the probability of the second.

Mutually Exclusive events are events that cannot happen at the same time.

b) given:

P(A) = # of heart cards in a deck / total number of cards

= 13 / 52

P(C) = # of face cards in a deck / total number of cards

= 12 / 52

P(A∩C) = (13/52) * (12/52)

= 1/13

check:

P(A∩C) = # of face cards in a deck who are also heart cards / total number of cards

= 4/52

= 1/13

Therefore events are independent.

c) given:

P(B) = # of diamond cards in a deck / total number of cards

= 13 / 52

P(C) = # of face cards in a deck / total number of cards

= 12 / 52

P(B∩C) = (13/52) * (12/52)

= 1/13

check:

P(B∩C) = # of face cards in a deck who are also diamond cards / total number of cards

= 4/52

= 1/13

Therefore events are independent.