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26 September, 11:49

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

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  1. 26 September, 15:08
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    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.
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