Question

A card is drawn from a pack of cards. What is the probability that the drawn card is neither a heart nor a king
A. \[\frac{4}{{13}}\]
B. \[\frac{9}{{13}}\]
C. \[\frac{1}{4}\]
D. \[\frac{{13}}{{26}}\]

Answer 1

Hint: The probability is a term that is a chance of getting a specific result from all the possible number of results. A pack of cards contains a total of 52 cards excluding joker cards.

Formula Used: \[P = \frac{n}{S}\], where P is the probability of getting a specific result, n is the result that we have to find and S is the sample space or the total possible outcomes.

Complete step-by-step answer: We know that a pack of cards contain 52 total cards out of which the 4 suits are spades, hearts, diamonds, and clubs, and each suit contains 13 different digits, from ace cards to king card.
We have to find the probability that the drawn card is neither a heart nor a king.
So, we know that the total number of cards that contain a heart is 13. So, we will subtract 13 from 52 as we don’t need the heart cards from the total number of cards, 52 - 13 = 39.
Now, we know that there are 4 suites and each suite contains 1 king, so there are a total number of 4 kings in a pack of cards. We have already removed all the heart cards at the starting, which means we also removed the king of hearts at the starting, so now the total number of the king cards that are present in the cards is 3. So, now we will subtract 3 from 39 as we also don’t need the king cards, 39 - 3 = 36.
Let n = 36 be our result, and S = 52 be the total number of cards we have. Let the probability of the drawn card be P.
Using the formula of probability we get the probability of the drawn card that is neither a heart nor a king as,
\[\begin{gathered}
  P = \frac{n}{S} \\
   \Rightarrow P = \frac{{36}}{{52}} \\
   \Rightarrow P = \frac{9}{{13}}
\end{gathered} \]



So, option B, \[\frac{9}{{13}}\] is the required solution.

Note: When we are counting the number of cards in our result, we can subtract the number of cards from a pack of cards that we don’t want instead of counting all the different numbers of cards that we want. Although both the methods will give the same result, subtracting the cards are much easier as their number is less compared to the cards that we want. While subtracting the cards, remember that we already removed the king of hearts while removing all the heart cards, so don’t again remove it while removing all the remaining king cards.