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)=?