After removing all of the clubs from a deck of cards, you are left with a 39 card deck with Hearts, Diamonds, and Spades. Answer the following questions assuming that after each draw of a card, that card is returned to this deck and reshuffled.

What is the probability of : A) drawing a red card? B) drawing a heart or a red card? C) drawing a jack or a red card?

(a) 2/3

(b) 2/3

(c) 9/13

Step-by-step explanation:

Total Number of Cards in new Deck=39

Hearts (Red) = 13

Diamonds (Red) = 13

Spades (Black) = 13

(a) P (drawing a red card)

Total number of red cards = 13+13=26

P (drawing a red card) = 26/39=2/3

(b) Drawing a heart or a red card

Number of Hearts=13

Number of red cards=26

Number of Red Hearts = 13

Since the two events are not mutually exclusive

P (Hearts or Red) = P (Hearts) + P (Red) - P (Hearts and Red)

P (H∪R) = P (H) + P (R) - P (H∩R)

=13/39 + 26/39 - 13/39

=26/39 = 2/3

(c) Drawing a jack or a red card.

Number of Jacks=3

Number of red cards=26

Number of Red Jacks = 2

Since the two events are not mutually exclusive

P (Jack or Red) = P (Jacks) + P (Red) - P (Jacks and Red)

P (J∪R) = P (J) + P (R) - P (J∩R)

=3/39 + 26/39 - 2/39

=27/39 = 9/13