One card is drawn at random from a well-shuffled deck of 52 cards. Fin

1.	One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a 4 (ii) a queen (iii) a black card.
Answer» (i) Total number cards in a deck = 52 Number of 4’s in a deck of cards = 4 Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\) ∴ Probability of drawing a 4 numbered card from the deck of cards P(4) = \(\frac{Numbe\,of\,4's\,in\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{4}{52}=\frac{1}{13}\) (ii) Total number cards in a deck = 52 Number of Queens in a deck of cards = 4 Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\) ∴ Probability of drawing a queen from the deck of cards P(queen) = \(\frac{Number\,of\,queen\,in\,a\,deck\,of\,cards}{Total\,number\,of\,in\,a\,deck}\) = \(\frac{4}{52}=\frac{1}{13}\) (iii) Total number cards in a deck = 52 Number of black cards in a deck of cards = 26 (13 spades and 13 clubs) Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\) ∴ Probability of drawing a black card from the deck of cards P(black) = \(\frac{Number\,of\,black\,cards\,in\,a\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{26}{52}=\frac{1}{2}\)

One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a 4 (ii) a queen (iii) a black card.

Answer»

(i) Total number cards in a deck = 52

Number of 4’s in a deck of cards = 4

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\)

∴ Probability of drawing a 4 numbered card from the deck of cards P(4)

= \(\frac{Numbe\,of\,4's\,in\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{4}{52}=\frac{1}{13}\)

(ii) Total number cards in a deck = 52

Number of Queens in a deck of cards = 4

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\)

∴ Probability of drawing a queen from the deck of cards P(queen)

= \(\frac{Number\,of\,queen\,in\,a\,deck\,of\,cards}{Total\,number\,of\,in\,a\,deck}\) = \(\frac{4}{52}=\frac{1}{13}\)

(iii) Total number cards in a deck = 52

Number of black cards in a deck of cards = 26 (13 spades and 13 clubs)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,in\,a\,deck}\)

∴ Probability of drawing a black card from the deck of cards P(black)

= \(\frac{Number\,of\,black\,cards\,in\,a\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{26}{52}=\frac{1}{2}\)