1. Probability and Odds
10.3

2. Vocabulary
Outcomes – the possible results Event – an outcome or collection of outcomes Probability – a number from 0 to 1 that tells the likelihood that something will occur. Can be written as a fraction, decimal or percent P=0 P=.5 P=1 will not equally likely will definitely occur to occur as not occur occur

3. Theoretical probability
If all outcomes for an event are equally likely, then the theoretical probability that event A will occur is: P(A) = number of outcomes in event A total number of outcomes The theoretical probability of an event is often just called the probability of the event
yes
total

5. Example
Roll a standard 6-sided die. What is the probability of rolling a five? There are 6 possible outcomes (total) Only 1 of the outcomes is a 5 (yes, that’s what I want) P(rolling a 5)=

7. Odds TOTAL = top + bottom
When all outcomes are equally likely, the odds in favor of an event are: Odds in favor = number of outcomes in A of event A number of outcomes not in A
yes no
TOTAL = top + bottom

8. Odds
When all outcomes are equally likely, the odds against an event are: no
yes
Odds against = number of outcomes not in A an event A number of outcomes in A

11. Experimental Probability
When an experiment is performed that consists of a certain number of trials, the experimental probability is given by:
P(A) = number of trials where A occurs
total number of trials

12. Geometric Probability
The ratio of two lengths, areas, or volumes Example: If it is equally likely that a parachutist will land anywhere on the rectangular field, then find the probability they will hit the square target.
298 yards
80 yards
140 yards

13. Geometric Probability
Example: If it is equally likely that a parachutist will land anywhere on the rectangular field, then find the probability she will hit the square target. P(square)=area of square = 6400 = 160 ≈ .15 area of rectangle 41,
298 yards
80 yards
140 yards