All GRE Subject Test: Math Resources
Example Question #1 : Sample Spaces
If I toss a coin 3 times, how many times will I roll at least one head?
None of the Above
Step 1: We need to find out how many outcomes there will be.
If we roll a coin three times, there are outcomes.
If we roll a coin times, there will be outcomes.
Step 2: Find all the outcomes.
The outcomes here are: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.
Step 3: In the list of outcomes, count how many times the letter H appears at least once.
The letter "H" appears in HHH, HHT, HTH, HTT, THH, THT, and TTH.
The letter "H" appears in of the outcomes.
The probability of getting at least one H in the outcomes in Step 2 is .
Example Question #2 : Sample Spaces
How many different combinations can i have when flipping a coin three times?
Step 1: Let's answer a smaller problem. How many ways can I toss one coin?
There are two ways, either I get Heads or Tails.
Step 2: How about two coins?
There are four ways... They are, HH, HT, TH, and TT
Step 3: How many different combinations for three coins?
Let's List them:
HHH, HHT, HTH, THH, TTT, THT, TTH, HTT
There are different combinations.