To find the probability of drawing a face card, we need to determine the number of face cards and the total number of cards in a standard deck.
Understanding Playing Cards
- A standard deck has 52 cards.
- Face cards are Jacks (J), Queens (Q), and Kings (K).
- Each rank (J, Q, K) appears in each of the 4 suits (Hearts, Diamonds, Clubs, Spades).
Calculating Favorable Outcomes
- Number of face card ranks = 3 (Jack, Queen, King).
- Number of suits = 4.
- Total number of face cards = Number of ranks × Number of suits = $3 \times 4 = 12$.
Calculating Probability
The formula for probability is:
$Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)$
- Number of Favorable Outcomes (drawing a face card) = 12.
- Total Number of Outcomes (drawing any card) = 52.
- Probability of drawing a face card = $\frac{12}{52}$.
Simplifying the Probability
The fraction $\frac{12}{52}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
- $12 \div 4 = 3$
- $52 \div 4 = 13$
- Simplified Probability = $\frac{3}{13}$.
Therefore, the probability of getting a face card is $\frac{3}{13}$.
Similar Questions
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Important Questions from Probability
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
What is the probability that all three boys sit together?
