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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

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.

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

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

Approved by eNotes Editorial Team