# MDM4U Probability – 2015-10-16

Today we started to learn the terms and the basics of probability. Some key terms:

Sample space: the set of all possible outcomes for a trial.

Probability experiment: a group of trials.

Trial: one part of a probability experiment; it generates an outcome.

Outcome: one possible result of a probability experiment.

Event: a set of outcomes.

For example, if your experiment is to roll a d6 die 50 times, a trial is one roll of a die. The sample space is $S=\{1,2,3,4,5,6\}$. One event, $E$, might be rolling an even number. Then $E=\{2,4,6\}$, and the probability of event $E$ occurring is $P(E)=\frac{3}{6}$.

We learned that a sample space is uniform if every outcome is equally likely (as they are in the example above). If the sample space is uniform, we can calculate the probability of event $A$ occurring as

$P(A)=\frac{n(A)}{n(S)}$

This doesn’t work if the sample space is not uniform. For example, if the experiment is to roll 2 dice 50 times, then the set of all possible outcomes is $S=\{2,3,4,5,6,7,8,9,10,11,12\}$. 7 is more likely to occur than 2, and so the sample space is not uniform and the formula above won’t work.