Question

pls answer this question I am having doubt​

Answer 1

Given Question:

From a well shuffled pack of playing cards, black jacks, black kings and black aces are removed. A card is then drawn from the pack. Find the probability of getting:

(i) a red card

(ii) a card that is not diamond

Solution:

Let's first write down some basic points to understand the question:

⇒ Total number of cards in a pack = 52

⇒ Number of black jacks = 2

⇒ Number of black kings = 2

⇒ Number of black aces = 2

⇒ Total number of black jacks, kings and aces = 2 + 2 + 2

    Total number of black jacks, kings and aces = 6

⇒ Number of cards left in the pack = Total number of cards - Total number of black jacks, kings and aces

   = 52 - 6

   = 46

Now, we can solve the question.

(i) A red card

The red cards in a deck refer to the diamond and heart cards.

⇒ Number of heart cards = 13

⇒ Number of diamond cards = 13

⇒ Total number of red cards = 13 + 13 = 26

So, probability of getting a red card:

$\sf{=Probability\:of\:getting\:a\:red\:card=\dfrac{Number\:of\:red\:cards}{Total\:no.\:of\:cards}}$

Here,

The total number of cards is 46 and the number of red cards is 26.

Therefore:

$\sf{=Probability\:of\:getting\:a\:red\:card=\dfrac{26}{46}}$

Simplifying the fraction:

$\sf{=Probability\:of\:getting\:a\:red\:card=\dfrac{13}{23}}$

No further simplifications can be done.

∴ The probability of getting a red card is 13/23.

(ii) Not a diamond card

⇒ Number of diamond cards in the pack = 13

⇒ Number of cards that are not diamond = Total number of cards - Number of diamond cards

   = 46 - 13

   = 33

So, probability of getting a card that is not diamond:

$\sf{=Probability\:of\:not\:\:getting\:a\:diamond\:card=\dfrac{Number\:of\:cards\:that\:are\:not\:diamond}{Total\:number\:of\:cards}}$

$\sf{=Probability\:of\:not\:\:getting\:a\:diamond\:card=\dfrac{33}{46}}$

No further simplifications can be done.

∴ The probability of not getting a diamond card = 33/46.