# In a standard deck of 52 cards, what are the odds of correctly identifying suit and number of two different cards with only 22 cards flipped over?

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Feb 3, 2018

$\frac{1}{435} = 0.0023$

#### Explanation:

$\text{I suppose you mean that there are 22 cards shown, so that}$
$\text{there are only 52-22 = 30 unknown cards.}$
$\text{There are 4 suits and every card has a rank, i assume that}$
$\text{this is what you mean by number as not all cards have a}$
$\text{number, some are face cards.}$

$\text{So two cards are picked out and someone must guess suit and}$
$\text{rank of them. The odds for that are}$

2 * (1/30) * (1/29) = 1/435 = 0.0023 = 0.23 %

$\text{Explanation : we know it is not one of the flipped over cards, so}$
$\text{there are only 30 possibilities for the first card and 29 for the}$
$\text{second card. We multiply the chances and multiply by 2}$
$\text{because the order of the two cards does not matter, so guessing}$
$\text{the second card first and then the first is also right.}$

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