What is the probability of getting a prime number in a deck of play cards, and the probability of getting an even number?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

The deck of a play card has 52 cards whcih are they:

4 sets of ( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K)

Let us determine the prime numbers in the set.

The prime number is an integer dividible by 1 and itself only:

The prime are: 2, 3, 5, 7

Then we had options of 4 numbers.

The deck of card has 4 sets of each number

Then the total of prime numbers in the deck of card is:

4 * 4 = 16 prime numbers:

Then the probability of getting a prime = 16/52 = 4/13

 

Now even numbers are: 2, 4, 6, 8, 10

Then there are  5 even numbers 4 times ;

==> total number of odd numbers  = 5*4 = 20

Then the probability of getting an even number = 20/52 = 5/13

kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

There are 52 numbers in a deck of cards with no jokers and assuming that the face cards have numeric values (i.e. a king is 13). To answer this quesition, you need to know how many of those cards are prime and how many are even.

The prime numbers less than 14 are:

2 3 5 7 11 13

That is, there are 6 of them, times 4 for each suit.
So your odds of getting a prime numbe are 6*4/52 = 46 %

Exactly half of the cards are even. Thus, your odds of getting an even number are 26/52 = 50%

If you wish to exclude the face cards from the deck, then repeat the calculation for prime numbers less than 10, and with 5 cards per suit being even.

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