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# To find the probability that a card drawn at random from a pack of 52 cards is neither a heart nor a king?(a)$\dfrac{4}{13}$ (b)$\dfrac{9}{13}$(c) $\dfrac{2}{13}$(d) $\dfrac{5}{13}$

Last updated date: 13th Jul 2024
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Hint: We start by finding the total possible number of outcomes possible for this problem. Since 1 card is drawn at random from a pack of 52 cards, the total possible number of outcomes is 52.
Now, to calculate the total number of desirable outcomes, we need to count the total number of cards from a pack of 52 cards that are neither a heart nor a king.

Now, according to the question, since the card is not a heart, it belongs to the remaining 3 suits (clubs, diamonds and spades). Out of these, since the card is not a king either, there are 12 desirable outcomes in each of these 3 suits (since one of the cards in the suits is a king, we remove this outcome). Now, we get the desired number of outcomes as $12\times 3=36$.
\begin{align} & \text{probability = }\dfrac{\text{total desirable outcomes}}{\text{total possible outcomes}} \\ & \text{probability = }\dfrac{\text{36}}{\text{52}} \\ & \text{probability = }\dfrac{\text{9}}{13} \\ \end{align}
Hence, the correct answer is (b) $\dfrac{9}{13}$.
\begin{align} & \text{probability = }\dfrac{\text{16}}{\text{52}} \\ & \text{probability = }\dfrac{4}{13} \\ \end{align}
Thus, Probability (card is neither a heart nor king) = $1-\dfrac{4}{13}=\dfrac{9}{13}$