Consider a standard deck of 52 cards Consider the following events when a card i

ID: 3175557 • Letter: C

Question

Consider a standard deck of 52 cards

Consider the following events when a card is randomly selected.

A: card selected is a king. B: card selected is a heart. C: card selected is a face card (i.e. J, Q, K) D: card selected is not a face.

Find the probabilities of:

a. P(A)

b. P(B)

c. P(C)

d. P(D)

e. P(A and B)

f. P(A|B)

g. P(B|A)

h. P(Bc |D)

i. P((C and B) c)

j. P(A or B)

k. P(B or C)

l. P(Ac or B)c)

m. Are A and B independent?

n. Are B and C independent?

o. Among all pairwise composite events “A and B”, “A and C”, “A and D”, “B and C”, “B and D”, and “C and D”, which ones are mutually exclusive?

a) P(A) = P(King) = 4/52 = 1/13

b) P(B) = P(Heart) = 13/52 = 1/4

c) P(C) = P(Face Card) = P(J, Q or K) = (4 + 4 + 4)/52 = 12/52 = 3/13

d) P(D) = P(Not a face card) = 1 - P(Face Card) = 1 - 3/13 = 10/13

e) P(A and B) = P(King and Heart) = 1/52

f) P(A | B) = P(King | Heart) = P(King and heart)/ P(Heart) = 1/13

g) P(B | A) = P(Heart | King) = P(Heart and king)/ P(King) = 1/4

h) P(Bc | D) = P(Not heart | Not a face card) = P(Not heart and not a face card)/ P(Not a face card) = 30/ 40 = 3/4

i) P((C and B)c) = 1 - P(C and B) = 1 - P(heart and face card) = 1 - 3/13 = 10/13

j) P(A or B) = P(A) + P(B) - P(A and B) = 1/13 + 1/4 - 1/52 = 4/13