You choose a card from a standard deck. What is the probability space for choosing a two?

Solution:
Step 1: Create the sample space. The sample space for this question is a list of all possible cards you could choose (H=hearts, D=diamonds, C=clubs, S=spades):
Ω = {AH,2H,3H,4H,5H,6H,7H,8H,9H,10H,JH,QH,KH, AD,2D,3D,4D,5D,6D,7D,8D,9D,10D,JD,QD,KD, AC,2C,3C,4C,5C,6C,7C,8C,9C,10C,JC,QC,KC, AS,2S,3S,4S,5S,6S,7S,8S,9S,10S,JS,QS,KS}.

Step 2: Assign probabilities. There are 52 choices in the sample space in Step 1. Each card has a 1/52 chance of being chosen.

Note that the question asked for the probability space and not the solution (i.e. it didn’t ask for the “probability of choosing a two.”) You could use the probability space for answering any question though. Just add up the probabilities. For example, the probability of choosing a two would be 1/52 + 1/52 + 1/52 + 1/52 = 4/52 = 1/13.