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Sagot :
A standard deck has 52 cards, there are four suits in the deck, "clubs", "diamonds", "hearts", and "spades". There are 13 ranks in each suit.
You know that the card drawn at random is a club. This means that there are 13 possible outcomes: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K.
→ You have to determine the probability of drawing an "8" given that the card is a club. There is only one 8 of clubs between the 13 cards of the suite, the probability is equal to the number of successes divided by the total number of outcomes:
[tex]P(8|Club)=\frac{1}{13}[/tex]→ You have to determine the probability of drawing a 10 or an ace, given that the card is a club. Once again, since you know that the card's suit is a club, you have to calculate the probability considering the 13 ranks that conform to the suit.
The events "drawing the 10 of clubs" and "drawing the ace of clubs" are mutually exclusive, which means that the probability of the union between both events is equal to the sum of their individual probabilities:
[tex]P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club)[/tex]There is only one 10 within the 13 ranks of the suit, the probability can be expressed as follows:
[tex]P(10|Club)=\frac{1}{13}[/tex]You can calculate the probability of drawing the Ace of Clubs using the same logic:
[tex]P(Ace|Club)=\frac{1}{13}[/tex]Now you can calculate the union between both events:
[tex]\begin{gathered} P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club) \\ P((10|Club)\cup(Ace|Club))=\frac{1}{13}+\frac{1}{13} \\ P((10|Club)\cup(Ace|Club))=\frac{2}{13} \end{gathered}[/tex]
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