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MATH / A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack,…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a face card (a Jack, Queen, or King)?
Plain-text mathematical notation (without MathML)
A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit.  Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red.  The deck is randomly arranged. What is the probability that the top card is a face card (a Jack, Queen, or King)?
Original LaTeX notation
A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit.  Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red.  The deck is randomly arranged. What is the probability that the top card is a face card (a Jack, Queen, or King)?

level

Level 3

type

Prealgebra

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Source and history

task_id
4de59527-b0dc-5055-9366-46d43a32d892
task_key
prealgebra--test--4de59527-b0dc-5055-9366-46d43a32d892
task_revision_id
1
config / split
prealgebra / test

Official source

initial import