3. Suppose you draw one card from a standard deck. Let A be the event the card d

Question

3. Suppose you draw one card from a standard deck. Let A be the event the card drawn is a diamond; let B be the event the card drawn is a club, and let C be the event the card drawn is a picture card (jack, queen, or king).

a. Are the events A and B mutually exclusive? Explain.

b. Are the events A and C mutually exclusive? Explain.

c. Describe in words the complement of C, which is labeled C’.

d. Find the probability of C and the probability of C’.

e. Find the probability of A or C, drawing a diamond or a picture card.

Explanation / Answer

a) Yes. A card cannot be diamond and club at the same time

b) No. Queesn of diamond is both A and C. So, A card can be both A and C at the same time

c) C' is the event that a card drawn is not a picture card

d) Number of picture cards = 3x4 = 12

P(C) = 12/52 = 3/13

P(C') = 1 - P(C)

= 1 - 1/13

= 12/13

e) P(A or C) = P(A) + P(C) - P(A and C)

P(A) = 1/4

P(C) = 3/13

P(A and C) = P(picture card of diamond) = 3/52

So, P(A or C) = 1/4 + 3/13 - 3/52

= 13/52 + 12/52 - 3/52

= 22/52

= 11/26

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