Recall that the sample space is the set of all possible outcomes. Theoretical probability can be found by comparing the number of favorable outcomes to the number of possible outcomes.
Theoretical Probability: 48, or 12 Sample Space:
cccc
H, H, H & H, H, T & H, T, H & H, T, T
T, H, H & T, H, T & T, T, H & T, T, T
Favorable Outcomes:
cccc
H, H, H & H, H, T & H, T, H & T, H, H
Practice makes perfect
We perform an experiment of flipping 3 coins. We are interested in finding the theoretical probability of getting at least 2 heads. Let's denote this event as A.
A: getting at least 2 heads
In order to obtain the desired probability, we need to find the number of favorable outcomes and compare it with the number of possible outcomes.
P( A) = Favorable Outcomes/Possible Outcomes
Recall that the sample space is the set of all possible outcomes. In this case, the sample space is the result of three stages.
First Coin Flip — Heads or Tails
Second Coin Flip — Heads or Tails
Third Coin Flip — Heads or Tails
The part that matters most is that the sample space ends up with all of the possible combinations. We will use H for Heads and T for Tails. Let's find the sample space.
Therefore, the number of possible outcomes in the sample space is 8 and all possible outcomes are listed below.
cccc
H, H, H & H, H, T & H, T, H & H, T, T
T, H, H & T, H, T & T, T, H & T, T, T
We can now focus on finding the favorable outcomes. Let's choose all the outcomes that result in getting at least 2 heads.
cccc
H, H, H & H, H, T & H, T, H & T, H, H
We found that the number of favorable outcomes is 4. We now have enough information to calculate the theoretical probability of getting at least 2 heads in 3 coin flips.
