Question

5. (10) A standard deck of cards contains 52 cards. (Round to THREE decimal places as needed.) Compute the probability of randomly selecting a heart or spade if one card is selected from the deck randomly a. Compute the probability of randomly selecting a heart or spade or club if one card is selected from the deck randomly. b. c. Compute randomly. the probability of randomly selecting a two or diamond if one card is selected from the deck d. If thr ee cards are selected from the deck randomly without replacement, compute the probability that the first is club, and second is heart, and third is spade.

Answer 1

5.

a.

Number of hearts + Number of spades = 13 + 13 = 26

Total number of cards = 52

Probability of randomly selecting a heart or spade if one card is selected from the deck randomly = 26/52 = 1/2 = 0.5

b.

Number of hearts + Number of spades + Number of club = 13 + 13 + 13 = 39

Total number of cards = 52

Probability of randomly selecting a heart or spade or club if one card is selected from the deck randomly = 39/52 = 3/4 = 0.75

c. Number of 'two' Cards = n(A) = 4

Number of diamond cards = n(B) = 13

Number of two and diamond card = n(A $\cap$ B) = 1

Total number of cards = 52

We use general formula for computing number of elements in the union or intersection of two sets:

$\large n(A\cup B) = n(A) + n(B) - n(A\cap B)$

Probability of randomly selecting a two or diamond if one card is selected from the deck randomly

= ( 4 + 13 - 1 ) / 52 = 16/52 = 4/13 = 0.3077

d.

Probability that the first is club = Number of clubs / total cards = 13/52

Now since one card has been drawn , so, total number of cards remaining in the deck will be 51

Probability that the second is heart = Number of hearts / total cards = 13/ 51

Now since 2 cards have been drawn , so, total number of cards remaining in the deck will be 50

Probability that the third is spade = Number of spades / total cards = 13/ 50

Probability that the first is club and second is heart and third is spade = (13/52) *(13/51) * (13/50)

= 0.01657