Explanation:
The number of spades on a standard deck of cards is
[tex]n(S)=13[/tex]
The number of aces on a standard deck of cards is
[tex]n(A)=4[/tex]
The number of ace of spade on a deck iof card is
[tex]n(A\cap S)=1[/tex]
The total number of cards in a standard deck of cards is
[tex]total=52[/tex]
The Probability of drawing ace or spade from a standard deck of cards
will be calculated using the formula below
[tex]P(AorS)=Pr(A)+Pr(S)-Pr(A\cap S)[/tex]
Where,
There are four aces in a deck of 52 cards, so the probability of drawing an ace is 4/52 = 1/13
Then, there are 13 spades in a deck, so the probability of drawing a spade is 13/52 or 1/4
But, since one of those aces is also a spade, we need to subtract that out so we're not counting it twice.
[tex]\begin{gathered} Pr(A)=\frac{4}{52} \\ Pr(S)=\frac{13}{52} \\ Pr(A\cap S)=\frac{1}{52} \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} P(AorS)=Pr(A)+Pr(S)-Pr(A\operatorname{\cap}S) \\ P(AorS)=\frac{4}{52}+\frac{13}{52}-\frac{1}{52} \\ P(AorS)=\frac{16}{52}=\frac{4}{13} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\frac{4}{13}[/tex]
The FOUTH OPTION is the correct answer
