Transcript 10.8 Geometric Probability - Fay's Mathematics [licensed

10.8 Geometric Probability
• Definition of Probability – the likelihood of an
event occurring.
• Usually written P(event)
• So if we’re talking about putting all names in
hat and pulling one out, the probability or
likelihood of my name being pulled out would
be written P(Mr. Fay).
• Then how would we determine the numerical
value?
• Favorable outcomes is the number of items in
your sample space that are aligned with the
desired (event).
• Number of possible outcomes is the number of
total items regardless of their alignment with the
(event). The number of possible outcomes is
often referred to as the SAMPLE SPACE.
• Probability can be written as a fraction (between
0 and 1) a decimal (between 0 and 1) or a
percentage between (0% and 100%).
• Geometric Probability – the use of geometric
models to solve certain types of probability
problems.
• In geometric probability points on a segment
or in a region of a plane represent outcomes.
• The geometric probability of an event is a
ratio that involves geometric measures such
as length or area.
EXAMPLE
What is then the probability that K does not lie on QR?
This concept is often referred to as the complement of an event. In particular if we
found P(K lies on QR), then P’(K lies on QR) is how we often would write the
complement of the event. Another method would be to rewrite the entire event as
P(K does not lie on QR). However, in probability/statistics it is often denoted with the
complement symbol ‘ instead of rewriting.
P’(event) = 1-P(event)
What does no more
than 5 minutes mean?
• When the points of a region represent equally likely
outcomes, you can find probabilities by comparing areas.
• P(shaded)=?
• P’(shaded)=?