This document discusses probability and events. It defines probability as a number between 0 and 1 that describes the likelihood of an event occurring. An event is a subset of possible outcomes from a chance process. The complement of an event is the opposite outcome where the event does not happen. It provides an example of predicting which cup contains bottled water. The frequency of an event is the number of times it occurs, and relative frequency is the frequency divided by the total number of trials. It instructs the reader to flip a coin and penny 10 times each to record results and compare predictions to actual outcomes. The probability of an event can be thought of as its long-run relative frequency over many trials.

1. Section 5.1

2. • A probability is a
number between zero
(never occurs) and
one (always occurs)
that describes the
likelihood of an event.
• An event is a subset
of the possible
outcomes in a chance
process.
• The compliment of
an event is the
opposite of the event.
That is, the even does
not happen.
Ex: Let W be the event that we predicted which cup had the bottled
water.
P(W) =
PC(W) =

3. • The number of times an event happens is known
as the frequency of that event. Our frequency
was ____
• The relative frequency is the value calculated
by dividing the number of times an event occurs
by the total number of times an experiment is
carried out (written as a fraction, decimal, or %).
Our relative frequency was ______

4. • Imagine that you were to flip a coin 10 times and write
down your results (use H for heads and T for tails)

5. • Flip a penny 10 times and record your results.
• Label your first list “predictions”
• Label your second list “actual”
• The probability of an event can be thought of
as its long-run relative frequency when the
experiment is carried out many times.

6. • Believers think that if you flip TTTTTT then the next flip of
a coin is more likely to be H. It is true that in the long run
heads will appear half the time. What is a myth is that
future outcomes must make up for any imbalance.
• Coins and dice have no memories!
• After 10,000 flips the result of the first six flips doesn’t
matter.