52 Deck Royalty Part 1 (Calculator Recommended)

Probability Level 1

Suppose I have a deck of 52 cards, and 51 of those cards were queens, while the remaining card is a Joker. If I were to arrange all of these cards at random, what's the probability (in percentage) that all of the 51 queens will be side-by-side?

(Round your answer to the nearest whole number)


The answer is 4.

Deva Craig by Deva Craig , 22, USA

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2 solutions

Mahdi Raza
Jun 2, 2020

\[\begin{align} \text{Total arrangements} &= 52 \quad [\color{blue}{\text{The number of unique places to place joker}}] \\ \text{Probable outcomes} &= 2 \quad [\color{blue}{\text{When joker is either first or last}}]

\end{align}\]

Probability = Probable outcomes Total arrangements = 2 52 ≈ 4 % \text{Probability } = \dfrac{\text{Probable outcomes}}{\text{Total arrangements}} = \dfrac{2}{52} \approx \boxed{4\%}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ron Gallagher
Jun 2, 2020

There are 52 places for the joker to go. Of those, the queens will all be together if the joker is either first or last (2 ways). The probability of this happening is 2/52, which rounds to 4%

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