A card is selected at random from a well-shuffled ordinary deck consisting of 13 spades, 13 clubs, 13 hearts, and 13 diamonds. 4 Jacks, 4 Queens, and 4 Kings are 'face' cards. The probability that the card is a heart or is a face card is about

(a) 0.23

(b) 0.42

(c) 0.19

(d) 0.48

(e) 0.25

b) 0.42

Step-by-step explanation:

Let A be the event that card is a heart card and B be the event that card is a face card.

We have to find P (A or B). P (A∪B) = ?

P (A∪B) = P (A) + P (B) - P (A∩B)

There are 13 heart cards and 12 cards are face cards. There would be 3 face card in hearts. So,

P (A) = 13/52=1/4=0.25

P (B) = 12/52=3/13=0.231

P (A∩B) = 3/52=0.058

P (A∪B) = 0.25+0.231-0.058

P (A∪B) = 0.481-0.058

P (A∪B) = 0.423

So, the probability that the card is a heart or is a face card is about is 0.42.