Class X Session 2023-24 Question 17

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 17

2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at

random from the remaining pack. What is the probability of getting a black card?

\begin{flalign} (a)\;\;& \frac{22}{52}\\ (b)\;\;& \frac{22}{46}&\\ (c)\;\;& \frac{24}{52}&\\ (d)\;\;& \frac{24}{46}&\\ \end{flalign}

Explanation : 

let's first determine the number of black cards in the original pack, and then subtract the number of hearts and spades removed.

In a standard deck of 52 cards, there are 26 black cards (13 spades and 13 clubs), 13 hearts, and 13 diamonds.

\[total\; number\; of\; remaining\; cards\; is\; = \; 11 + 9 + 13 + 13 \]

After removing 2 hearts and 4 spades, we are left with

11 hearts (13 - 2)

9 spades (13 - 4)

13 clubs (unchanged)

13 diamonds (unchanged)

\[total\; number\; of\; remaining\; cards\; is\; = \; 11 + 9 + 13 + 13 \]

there are 22 black cards (9 spades and 13 clubs)

So, the probability of drawing a black card from the remaining pack will be 

\[P(Black \; card) = \; \frac {No \; of \; black\; card}{Total \; number \; of \; remaining\; card\;} \; = \; \frac{22}{46}\]

Guess the Option and comment below  👇