Question

A card is drawn at random from a standard 52-card deck. Find the following probabilities: (2 points) a. The probability the card is a diamond or a face card. (2 points) b. The probability that the card is neither an ace nor a heart. (2 points) c. The probability that the card is a face card or a 3

Answer 1

(a)
`(11)/(26)`

(b)
`(9)/(13)`

(c)
`(4)/(13)`

Explanation:

Number of cards in a Standard Deck=52

(a)

Number of Diamonds (D)=13

Number of Face Cards(F) = 12

Number of Diamonds that are face cards = 3

`Pr($that the card is a diamond or a face card)=P(D)+P(F)-P(D \cap F)\\=(13)/(52) +(12)/(52) -(3)/(52) \\=(22)/(52) \\=(11)/(26)`

(b)The probability that the card is neither an ace nor a heart.

Number of Aces (A)=4

Number of Hearts(H) = 13

Number of Hearts that are Aces = 1

`Pr($that the card is a Ace or a Heart), P(A \cup H)=P(A)+P(H)-P(A \cap H)\\=(4)/(52) +(13)/(52) -(1)/(52) \\=(16)/(52) \\$Therefore, probability that the card is neither an ace nor a heart.\\=1-P(A \cup H)\\=1-(16)/(52)\\=(36)/(52)\\=(9)/(13)`

(c)The probability that the card is a face card or a 3

Number of 3 cards(T)=4

Number of Face Cards(F) = 12

`Pr($that the card is a three or a face card)=P(T)+P(F)\\=(4)/(52) +(12)/(52) \\=(16)/(52) \\=(4)/(13)`