Question

From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.

& A.\dfrac{2}{52} \\\ & B.\dfrac{1}{52} \\\ & C.\dfrac{2}{13} \\\ & D.\dfrac{1}{26} \\\ \end{aligned}$$

Answer 1

In this question, we need to find the probability of picking a jack or a king from a pack of cards. For this, we will first understand the number of cards of a type in the deck of cards and then find the number of jacks and kings in the deck. Number of jacks and king will give us the number of favorable outcomes. Since a deck of cards has 52 cards, the total outcome will be 52. Probability is given as $\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total number of outcomes}}$.

Complete step by step answer:
Here we have to find the probability of getting a jack or a king from a deck of cards. In a deck of cards, we have a total of 52 cards so the total number of outcomes will be equal to 52.
Let us understand the type of cards in a deck.
We have four sets of cards called heart, spade, club and diamond. Every set has 13 cards of the number A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. Since every set has every such number of cards. So the number of kings (K) will be four. Similarly, the number of jacks (J) will also be four.
Hence we have a favorable outcome as 4+4 = 8.
We know that probability is given by, $\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total number of outcomes}}$.
And for this question, favorable outcomes are 8 and total number of outcomes are 52. So our required probability will be: $\text{Probability}=\dfrac{\text{8}}{\text{52}}$.
Let us simplify it. Dividing the numerator and denominator by 4 we get: $\dfrac{2}{13}$.
Hence our required probability is $\dfrac{2}{13}$.

So, the correct answer is “Option C”.

Note: Students should know all the types of cards that a deck has to solve these questions. Note that, there are four cards for every number. Hence, for kings we have four kings which are king of heart, king of spade, king of club and king of diamond. Similarly, we have four jacks. Probability always lies between 0 and 1.