A card is drawn from a pack of 52 cards. Find | vedclass

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(D) Let $A$ be the event of getting a spade card,$B$ be the event of getting an ace card,and $C$ be the event of getting a red card.The total number o

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$\frac{10}{13}$

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(D) Let $A$ be the event of getting a spade card,$B$ be the event of getting an ace card,and $C$ be the event of getting a red card.The total number of cards is $52$.$P(A) = \frac{13}{52}$,$P(B) = \frac{4}{52}$,$P(C) = \frac{26}{52}$.Intersection probabilities:$P(A \cap B) = \frac{1}{52}$ (the ace of spades).$P(B \cap C) = \frac{2}{52}$ (the ace of hearts and the ace of diamonds).$P(C \cap A) = 0$ (a card cannot be both red and a spade).$P(A \cap B \cap C) = 0$.Using the inclusion-exclusion principle:$P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(B \cap C) - P(C \cap A) + P(A \cap B \cap C)$$= \frac{13}{52} + \frac{4}{52} + \frac{26}{52} - \frac{1}{52} - \frac{2}{52} - 0 + 0$$= \frac{13 + 4 + 26 - 1 - 2}{52} = \frac{40}{52} = \frac{10}{13}$.

$A$ card is drawn from a pack of $52$ cards. Find the probability of getting a spade,an ace,or a red card.

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