- An experiment is a controlled operation that yields
a set of results.
- For example, flip a coin 10 times and record the number of times it landed on "heads".
- The possible results of an experiment are called the outcomes
- In the above experiment, the outcomes are heads or tails
- An event is a sub-collection of the outcomes of an experiment.
- The theoretical probability of an event is determined by a study of the possible outcomes that can occur for a given experiment.
- The empirical probability of an event is the ratio of the times an even occurred to the number of experiments that were conducted.
-
total number of times event E occurred
P(E) = -------------------------------------------------
total number of times the experiment was conducted
- Example 1
Toss a 6 sided die 20 times recording the result each time.
Result Freq P(n)
1 4 4/20 .2
2 5 5/20 .25
3 1 1/20 .05
4 3 3/20 .15
5 5 5/20 .25
6 2 2/20 .1
Let E be the event the result was odd
P(E) = P(1) + P(3) + (5) = .2 + .05 + .25 = .5
- Example 2, problem 16 page 660
24 rock
16 country
8 classical
12 other
Let E be the event that the person selected rock
# that selected rock
P(E) = -------------------
total customers
Total = 24 + 16 + 8 + 12 = 60
P(E) = 24/60 = .4 or 40%
- The Law of Large Numbers states that probability statements apply in practice to a large number of trials, not to a single trial.
- We can't predict a single outcome, just if it is likely or not.
- Or, we can say how likely each possible outcome is, just not which one will occur.
- Example 3
I have two children, they are both girls.
The chances of this happening are 1 in 4 or 25%.
If we have another child
A. What are the chances she will be a girl?
1 in 2 or 50%
B. What are the chances of 3 girls in a row?
1 in 8 or 12.5%
C. What will the child be?