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. One card is drawn at random. What is the probability that it is neither a heart nor a face card?

\frac{27}{52}

Correct answerYour answer

\frac{15}{26}

Correct answerYour answer

\frac{3}{4}

Correct answerYour answer

\frac{10}{13}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Cards that are a heart or a face card: 13 hearts + 12 face cards − 3 face cards that are hearts = 22.
Neither: $52 - 22 = 30$ .
Probability $= \frac{30}{52} = \frac{15}{26}$ .

Worth noting

$\frac{27}{52}$ removes all 12 face cards from the 39 non-hearts, but only 9 face cards are not hearts. $\frac{3}{4}$ ignores the face-card condition, and $\frac{10}{13}$ ignores the heart condition.

Concept: Complement of a union ('neither … nor')
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.

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. One card is drawn at random. What is the probability that it is neither a heart nor a face card?

Explanation