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
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 boys and girls sit alternatively?
What is the probability that P and Q take the two end positions?
