A card is drawn from a standard deck of 52 cards. What is the ... | Mathematics MCQ | Examoogle

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MathematicsStatistics and Probability

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a red queen?

$\frac{1}{26}$

$\frac{1}{52}$

$\frac{2}{13}$

$\frac{1}{13}$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsStatistics and Probability

Option A

$\frac{1}{26}$

Quick Summary:

Directly identify that there are 2 red queens in a 52-card deck and reduce the fraction immediately.

📐MAMath SolutionDirect Formula

📋 Given

Total number of cards in a standard deck = 52, Number of red queens = 2

🔢 Formula Used

P=n(E)n(S)P = \frac{n(E)}{n(S)}P=n(S)n(E)​

⚡ Exam Hall Shortcut / Speed Trick

Directly identify that there are 2 red queens in a 52-card deck and reduce the fraction immediately.

⚠️ Common Student Trap / Pitfall

Confusing red queens (2) with all queens (4) or all red cards (26).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Sample Space

A standard deck of playing cards contains a total of $52$ cards, representing the total number of possible outcomes.

n(S)=52n(S) = 52n(S)=52

Identify Favorable Outcomes

There are two red suits (Hearts and Diamonds), and each suit has one queen. Therefore, the number of red queens is $2$ .

n(E)=2n(E) = 2n(E)=2

Calculate Probability

Substitute the values into the probability formula and simplify the fraction.

P=252=126P = \frac{2}{52} = \frac{1}{26}P=522​=261​

✅

A is correct because the probability of drawing a red queen is $\frac{2}{52}$ , which simplifies to $\frac{1}{26}$ .

Core Concepts Used

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💡 EXAM TIP

Memorizing the breakdown of a standard 52-card deck (suits, colors, face cards) saves valuable time in quantitative aptitude exams.

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