Question

A standard deck of cards has 52 cards and 4 suits (2 red and 2 black), as shown in the picture: Standard deck of 52 cards 4 suits (CLUBS, SPADES, HEARTS, DIAMONDS 13 CLUBS 13 SPADES 13 HEARTS 13 DIAMONDS

Before each draw the deck is well shuffled and a single card randomly drawn. (Use 4 decimals for all answers)
A. What is the probability that the first card drawn is a face card (a Jack, a Queen, or a King)?

B. What is the probability that the second card drawn is red?

C. What is the probability that the first card drawn is a face-card AND the second card drawn is red?

D. What is the probability that the first card drawn is NOT a face card?

Now three draws are made, with the card replaced and the deck reshuffled each time.
E. What is the probability that all three cards are face cards?

F. What is the probability that none of them are face cards?

G. What is the probability that at least one of the three cards is a face card?

H. Which of the following are examples of disjoint events? Choose all that apply. a. Drawing a 6 and drawing a heart. b. Drawing a 7 and drawing a face card. c. Drawing a 10 and drawing a red card. d. Drawing a 9 and drawing an Ace.

Answer 1

A) P(face card) = 12/52

= 0.2308

B) P(second card is red) = 26/52

= 0.5

C) P(first card is face card and second card is red) = P(first card is red face card and second card is red) + P(first card is black face card and second card is red)

= 6/52 x 25/51 + 6/52 x 26/51

= 0.1154

D) P(not face card) = 1 - P(face card)

= 1 - 0.2308

= 0.7692

E) P(all three are face cards) = 0.2308³

= 0.0123

F) P(none are face cards) = 0.7692³

= 0.4551

G) P(at least one of the three is face card) = 1 - P(no face cards)

= 1 - 0.4551

= 0.5449

H) Disjoint events are the events which cannot occur simultaneously

The following events are disjoint

b. Drawing a 7 and drawing a face card

d. Drawing a 9 and drawing an ace