The Quirkdeck

Probability Level pending

Sean have a strange french card deck, that he calls, simply, the Quirkdeck . In the deck there are:

8 aces , two for each suit
6 kings , two of clubs, two of spades, and one for both hearts and diamonds
6 queens , two of hearts, two of spades, and one for both clubs and diamonds
5 jacks , two of diamonds and one for each other suit
5 jolly-jokers
12 other cards , that are numbers of all suits, that we can call "common cards"

So he have overall 52 cards. Now he plays a game: he writes on a paper which card he find over the deck, and put this card in a second deck. After ten round, you can read on he's paper that he find: 2 aces (one of spades and one of diamonds), 3 kings, 3 common cards and only one for both jacks and jokers.

What's the probability that now he find an other ace?

And what's the probability that it's the last spades ace?

\frac{6}{42}

and

\frac{2}{42}

\frac{6}{42}

and

\frac{1}{42}

\frac{8}{42}

and

\frac{2}{42}

\frac{6}{52}

and

\frac{1}{42}

\frac{2}{42}

and

\frac{1}{42}

1 solution

Giovanni Delta
Dec 1, 2018

We know that there are 52 cards in the Strangedeck. Sean take off 10 of these, so now we have 42 cards in the deck. We also know that there are 8 aces and that 2 were take off. So now we have 6 aces out of 42 cards.

The probability it's of course $\frac{6}{42}$ .

The second quest it's easier: we know that now we have only a spade ace in the deck.

So the probability it's only $\frac{1}{42}$ .

The Quirkdeck

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