Answer:
(a)[tex]\dfrac{11}{26}[/tex]
(b)[tex]\dfrac{9}{13}[/tex]
(c)[tex]\dfrac{4}{13}[/tex]
Step-by-step 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
[tex]Pr($that the card is a diamond or a face card)=P(D)+P(F)-P(D \cap F)\\=\dfrac{13}{52} +\dfrac{12}{52} -\dfrac{3}{52} \\=\dfrac{22}{52} \\=\dfrac{11}{26}[/tex]
(b)The probability that the card is neither an ace nor a heart.
Number of Aces (A)=4
Number of Hearts(H) = 13
Number of Hearts that are Aces = 1
[tex]Pr($that the card is a Ace or a Heart), P(A \cup H)=P(A)+P(H)-P(A \cap H)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\$Therefore, probability that the card is neither an ace nor a heart.\\=1-P(A \cup H)\\=1-\dfrac{16}{52}\\=\dfrac{36}{52}\\=\dfrac{9}{13}[/tex]
(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
[tex]Pr($that the card is a three or a face card)=P(T)+P(F)\\=\dfrac{4}{52} +\dfrac{12}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]
