To obtain the experimental probability of the event, divide the number of successes by the number of trials. While in order to find the theoretical probability of an event calculate the ratio of the number of favorable outcomes to the number of possible outcomes.
TH
Practice makes perfect
We flipped two coins 12 times. The table shows the results of the experiment. Let H stand for Heads and T stand for Tails.
Since we have the results of the experiment, in order to calculate the experimental probability of the event, we need to divide the number of successes by the number of trials.
P(Event)=Number of Successes/Number of Trials
In our case, the number of trials is equal to 12 because we flipped the coins 12 times. The number of successes is the number of times a particular outcome has occurred. This information was given to us in the table. Let's find the experimental probabilities.
HH
HT
TH
TT
Number of Successes
2
6
3
1
Probability
P(HH) = 2/12
P(HT) = 6/12
P(TH) = 3/12
P(TT) = 1/12
Simplify
P(HH) = 1/6
P(HT) = 1/2
P(TH) = 1/4
P(TT) = 1/12
The Theoretical Probability
The theoretical probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.
P(Event)=Favorable Outcomes/Possible Outcomes
We have 4 possible outcomes: HH, HT, TH, and TT. Consequently, in each case there is only 1 favorable outcome. Therefore, the theoretical probability for all of the events is the same.
HH
HT
TH
TT
Probability
P(HH) = 1/4
P(HT) = 1/4
P(TH) = 1/4
P(TT) = 1/4
Comparison
Let's sum up both the experimental probability and the theoretical probability.
Probability
P(HH)
P(HT)
P(TH)
P(TT)
Experimental
1/6
1/2
1/4
1/12
Theoretical
1/4
1/4
1/4
1/4
We found that TH is the outcome for which the experimental probability is the same as the theoretical probability.
