What is the probability of drawing a Jack from a deck of 52 cards?

Question

What is the probability of drawing a Jack from a deck of 52 cards?

 

If the two Jokers are placed into this deck of cards, how does that change the probability of the drawing?

Answer 1

Hello, thank you for taking the time to post your question!

There are 4 jacks and 52 cards in a standard deck so the probability is

4/52 = 1/13 , meaning that you have a 1/13 chance of drawing a Jack from a deck of 52 cards

The addition of the jokers just changes the denominator because now there are 52 + 2 = 54 total cards that you are drawing from

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

If there are 52 cards, and 2 of them are Jacks, the probability of drwaing a Jack is 2 out of 52, because there are 2 Jacks out of the 52 cards you have total. (You can reduce the fraction 2/52 to 1/26 by dividing both the numerator and denominator by 2/2 which equals 1, because 2/2 is a factor of 1, and the only factor of 1 is 1 itself, so the 2/2 you are dividing by is really 1, so you are not changing the fraction 2/52.)

 

 

If there are no Jacks in a pile of 52 cards, and 2 cards of Jacks are added, then your probability to randomly draw out a Jack will decrease because there are more cards to choose from.

 

This decreases the probability to 2 out of 54 (or 2/54) which is equal to out of 27, or 1/27, if you divide the numerator and denominator of 2/54 by 2/2.

 

If there are 2 Jacks in a pile of 52 cards already, and you add two more Jacks, then your probablilty of drawing out a Jack is 4 out of 54 (or 4/54), and when you divide the numerator and denominator by 2/2 (because it's a factor of 1, so you don't change the equation), you get 2/26.

 

2 out of 26 is greater than the original 1 out of 26, and also greater than 1 out of 27. (Because 27 is greater than 26, there are fewer chances to draw out the one card that is a Jack from the pile of 27 cards.)

 

2 out of 26 is also greater than the 1 out of 26, because you have two chances out of 26 to draw a jack rather than one. 

 

So 1 out of 27 is less than 1 out of 26, which is less than 2 out of 26.