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# One card is drawn from a well-shuffled deck of $52$ cards. Calculate the probability that the card will not be an ace.

Last updated date: 20th Jun 2024
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Hint: Find number of all non ace cards from a deck of $52$ cards which are your favorable outcomes, then divide it by the total number of outcomes to get the required probability.
* Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.

Find the total outcomes.
We have a total of $52$ cards in a well-shuffled deck.
$\therefore$ Total outcomes $= 52.$
Find the favorable outcomes.
There are $4$ ace cards in a deck of $52$ cards.
$\therefore$ Total non-ace cards $= 52 - 4 = 48.$
$\therefore$ Total favorable outcomes $= 48.$
Find the probability that the card will not be an ace by using a probability formula.
Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.
Probability ${\text{ = }}\dfrac{{{\text{48}}}}{{{\text{52}}}}$
Cancelling out common factors from numerator and denominator.
$= \dfrac{{12}}{{13}}$
$\therefore$ Probability that the card will not be an ace $= \dfrac{{12}}{{13}}$.

Note: Students can get confused with ace and non-ace cards. Keep in mind the ace cards are the four cards each of different suites, having A written on them along with the sign of the suite. So, all other cards except these are non-ace cards.
Alternate method:
Probability that the card will not be an ace $= 1 -$ Probability that the card will be an ace
There are $4$ ace cards in a deck of $52$ cards.
Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.
Probability $= \dfrac{4}{{52}}$.
Probability that the card will not be an ace $= 1 -$ Probability that the card will be an ace
$= 1 - \dfrac{4}{{52}} \\ = \dfrac{{52 - 4}}{{52}} \\ = \dfrac{{48}}{{52}} \\ = \dfrac{{12}}{{13}} \\$
Probability that the card will not be an ace $= \dfrac{{12}}{{13}}$.