Probability Calculation for Spade Card
This solution details the steps to find the probability of drawing a spade card after specific cards are removed from a standard 52-card deck.
Initial Deck Overview
- A standard deck contains 52 playing cards.
- These cards are divided into 4 suits: Spades (♠), Hearts (♥), Diamonds (♦), and Clubs (♣).
- Each suit comprises 13 cards (A, 2, 3, ..., 10, J, Q, K).
- The black suits are Spades and Clubs.
Identifying Removed Cards
The question specifies removing Kings and Queens of black colour. These are:
- King of Spades (K♠)
- Queen of Spades (Q♠)
- King of Clubs (K♣)
- Queen of Clubs (Q♣)
In total, 4 cards are removed from the deck.
Determining the Remaining Cards
The total number of cards left in the deck after the removal is calculated as:
Remaining Cards = Total Cards - Removed Cards
Remaining Cards = $52 - 4 = 48$
Counting Remaining Spade Cards
A standard deck begins with 13 spade cards. The removal process eliminated two spade cards:
- King of Spades (K♠)
- Queen of Spades (Q♠)
The number of spade cards still in the deck is:
Remaining Spades = Initial Spades - Removed Spades
Remaining Spades = $13 - 2 = 11$
Calculating the Final Probability
Probability is calculated as the ratio of favorable outcomes to the total possible outcomes.
In this case:
- Favorable Outcomes = Number of remaining spade cards = 11
- Total Possible Outcomes = Total remaining cards = 48
The probability of drawing a spade card is:
Probability(Spade) = $\frac{\text{Number of Remaining Spades}}{\text{Total Number of Remaining Cards}} = \frac{11}{48}$
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