Question

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?

Answer 1

Answer:

(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