A standard deck has 52 cards in 4 suits of 13 (ace, 2 to 10, jack, queen, king); hearts and diamonds are red, clubs and spades are black, and the jack, queen and king are the face cards. Two cards are drawn together at random (without replacement). What is the probability that one is red and the other is black?

\frac{26}{51}

Correct answerYour answer

\frac{25}{51}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

\frac{13}{51}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Ways to draw 2 cards: ${}^{52}C_{2} = 1326$ .
One red and one black: $26 \times 26 = 676$ .
Probability $= \frac{676}{1326} = \frac{26}{51}$ .

Worth noting

$\frac{1}{2}$ is the answer WITH replacement $\left(2 \times \frac{1}{2} \times \frac{1}{2}\right)$ . $\frac{25}{51}$ is P(same colour), and $\frac{13}{51}$ counts only the order red-then-black.

Concept: Mixed-colour draw without replacement
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsCoins, dice and cards

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Ten questions from Counting and Basic Probability, at your own pace.

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