Question

The king, the jack and 10 of spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling. Find the probability of getting a red card.
(A). $$\dfrac{26}{40}$$
(B). $$\dfrac{24}{40}$$
(C). $$\dfrac{20}{40}$$
(D). $$\dfrac{13}{40}$$
(This question has multiple correct option)

Answer 1

Hint: In this question it is given that the king, the jack and 10 of spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling. We have to find the probability of getting a red card. So to find the probability we need to know that,
$$\text{probability} =\dfrac{\text{Number of favourable outcomes} }{\text{Total number of outcomes} }$$.....(1)
Complete step-by-step solution:
If a king, a jack and 10 spades are lost then the total number of lost cards= (1+1+10)=12
We know that in a deck there are 52 cards, if 12 cards got lost then the remaining cards are (52-12)=40 cards,
So we have to select the red cards from the remaining 40 cards.
There, total number of outcomes = 40.
In a deck of 52 cards there are 26 red cards,

Case-1,
Now if the lost king and jack are from red cards then we have remaining 24 red cards.
So that means we have to find the probability of selecting red cards from the 40 cards,
Therefore, favorable outcome = 24
So the probability = $$\dfrac{24}{40}$$

Case-2,
If the king and jack are not from red cards, then we have 26 red cards in a deck.
So our favourite outcome = 26.
Therefore the probability of selecting red cards = $$\dfrac{26}{40}$$.
Hence the correct option is A and B.

Note: While solving any card related problem you need to know that the standard deck of cards contains 52 cards. It includes 13 ranks in each of the four French suits: clubs (black), diamonds (red), hearts (red) and spades (black), with reversible "court" or face cards. Each suit includes an Ace, a King, Queen and Jack, each depicted with a symbol of its suit; and ranks two through 10.