If a card is drawn at random from a pack of 5 | vedclass

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Question

(C) Let $A$ be the event that the card drawn is a king and $B$ be the event that the card drawn is a diamond.Total number of cards = $52$.Number of ki

Vedclass · Accepted Answer

$\frac{4}{13}$

Vedclass · Answer

(C) Let $A$ be the event that the card drawn is a king and $B$ be the event that the card drawn is a diamond.Total number of cards = $52$.Number of kings $n(A) = 4$,so $P(A) = \frac{4}{52}$.Number of diamonds $n(B) = 13$,so $P(B) = \frac{13}{52}$.The king of diamonds is common to both,so $n(A \cap B) = 1$,and $P(A \cap B) = \frac{1}{52}$.Using the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$P(A \cup B) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52}$.Simplifying the fraction: $\frac{16}{52} = \frac{4}{13}$.

If a card is drawn at random from a pack of $52$ cards,the probability that the card is a king or a diamond is $..........$.

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