The king queen and Jack of clubs are removed from a deck of 52 playing card, and the remaining card are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (1)heart (2)queen (3)club ?

Question

Answer

Given total no. of cards = 52
no. of cards removed = 3
remaining cards = 52 - 3 = 49

1. a heart

fav outcomes = 13

p( heart ) = favourable out comes / total outcomes
= 13/49

2.a queen

no. of fav outcomes = 3

p( queen) = favourable outcomes/total outcomes
= 3/49

3. a club

fav outcomes = 13-3
=10

p( club) = favourable outcomes/ total outcomes
= 10/49

That's all🙂

Answer

Preliminary Information:

- A standard deck of playing cards consists of 52 cards.
- Each deck includes 4 suits: hearts, diamonds, clubs, and spades.
- Each suit contains 13 cards: Ace, 2-10, Jack, Queen, and King.

Step 1: Determine the Total Number of Remaining Cards

To calculate the probability, we need to determine the number of remaining cards in the deck after removing the King, Queen, and Jack of clubs.
Total number of cards in a deck = 52
Number of removed cards = 3 (King, Queen, and Jack of clubs)
Remaining cards = Total cards - Removed cards = 52 - 3 = 49

Step 2: Calculate the Probability of Drawing a Heart

- Number of hearts in a deck = 13
- Number of hearts removed = 0 (since we only removed clubs)
- Remaining hearts = Number of hearts - Hearts removed = 13 - 0 = 13
- Probability of drawing a heart = Number of hearts / Remaining cards = 13 / 49 = 13/49 or approximately 0.2653

Step 3: Calculate the Probability of Drawing a Queen

- Number of queens in a deck = 4 (one for each suit)
- Number of queens removed = 1 (Queen of clubs)
- Remaining queens = Number of queens - Queens removed = 4 - 1 = 3
- Probability of drawing a queen = Number of queens / Remaining cards = 3 / 49 = 3/49 or approximately 0.0612

Step 4: Calculate the Probability of Drawing a Club

- Number of clubs in a deck = 13
- Number of clubs removed = 3 (King, Queen, and Jack of clubs)
- Remaining clubs = Number of clubs - Clubs removed = 13 - 3 = 10
- Probability of drawing a club = Number of clubs / Remaining cards = 10 / 49 ≈ 0.2041

Summary:

The probabilities of drawing different cards from the remaining deck are as follows:
- Probability of drawing a heart: 13/49 or approximately 0.2653
- Probability of drawing a queen: 3/49 or approximately 0.0612
- Probability of drawing a club: 10/49 or approximately 0.2041

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