Answer
Verified
479.7k+ views
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.
Complete step-by-step answer:
To calculate this, we know that there are four suits of cards – clubs, diamonds, spades and hearts. Each suit contains 13 cards. (totalling up to 52 cards)
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 $12\times 3=36$.
Now,
$\begin{align}
& \text{probability = }\dfrac{\text{total desirable outcomes}}{\text{total possible outcomes}} \\
& \text{probability = }\dfrac{\text{36}}{\text{52}} \\
& \text{probability = }\dfrac{\text{9}}{13} \\
\end{align}$
Hence, the correct answer is (b) $\dfrac{9}{13}$.
Note: An alternative way to solve the problem is to subtract the possible number of outcomes for which a card drawn is a heart and king from 1. To explain,
Probability (card is heart and king) + Probability (card is neither a heart nor king) = 1
Thus,
Probability (card is neither a heart nor king) = 1 - Probability (card is heart and king)
Now, for the card to belong to hearts suit, there are 13 possible outcomes. Further, for a card to be a king, there are 4 possible outcomes. However, out of these 4 outcomes, 1 of the outcomes is common with 13 outcomes of heart suit. (thus, this outcome is removed). We are thus left with 13+4-1=16 outcomes.
Thus,
$\begin{align}
& \text{probability = }\dfrac{\text{16}}{\text{52}} \\
& \text{probability = }\dfrac{4}{13} \\
\end{align}$
Thus, Probability (card is neither a heart nor king) = $1-\dfrac{4}{13}=\dfrac{9}{13}$
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.
Complete step-by-step answer:
To calculate this, we know that there are four suits of cards – clubs, diamonds, spades and hearts. Each suit contains 13 cards. (totalling up to 52 cards)
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 $12\times 3=36$.
Now,
$\begin{align}
& \text{probability = }\dfrac{\text{total desirable outcomes}}{\text{total possible outcomes}} \\
& \text{probability = }\dfrac{\text{36}}{\text{52}} \\
& \text{probability = }\dfrac{\text{9}}{13} \\
\end{align}$
Hence, the correct answer is (b) $\dfrac{9}{13}$.
Note: An alternative way to solve the problem is to subtract the possible number of outcomes for which a card drawn is a heart and king from 1. To explain,
Probability (card is heart and king) + Probability (card is neither a heart nor king) = 1
Thus,
Probability (card is neither a heart nor king) = 1 - Probability (card is heart and king)
Now, for the card to belong to hearts suit, there are 13 possible outcomes. Further, for a card to be a king, there are 4 possible outcomes. However, out of these 4 outcomes, 1 of the outcomes is common with 13 outcomes of heart suit. (thus, this outcome is removed). We are thus left with 13+4-1=16 outcomes.
Thus,
$\begin{align}
& \text{probability = }\dfrac{\text{16}}{\text{52}} \\
& \text{probability = }\dfrac{4}{13} \\
\end{align}$
Thus, Probability (card is neither a heart nor king) = $1-\dfrac{4}{13}=\dfrac{9}{13}$
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE