warm up write the converse, inverse, and contrapositive of: “if m is the midpoint of ab, then m,...
TRANSCRIPT
Warm Up
Write the converse, inverse, and contrapositive of:
“If M is the midpoint of AB, then M, A, and B are collinear.”
Are these statements true or false?
• Converse: If M, A, and B are collinear, then M is the midpoint of AB
• Inverse: If M is not the midpoint of AB, then M, A, and B are noncollinear.
• Contrapositive: If M, A, and B are noncollinear, then M is not the midpoint of AB.
False
False
True
ProbabilityProbability
How to solve probability.How to solve probability.
Where do we use probability?
Insurance companies, card players, casino, lottery etc…
Who uses probability?
Doctors, secretaries, accountants, programmers, and GEOMETRY STUDENTS! Just to name a few.
Setting up and solving probability problems requires precise and orderly organized thinking skills.
Probability is not part of geometry but rather statistics. However, you will see problems in the “Problems Sets” that deal with it, so follow these two basic
steps:
1. Determine all possibilities in a logical manner. Count them.
2. Determine the number of these possibilities that are “favorable”. We shall call these winners.
List all possibilities:
A B C D
Calculate Probability:Probability = number of winners
number of possibilities
Ex. 1a. If one point is picked at random from the given figure, what is the probability that it is on the angle?
AB
C
D circle the winners.
P= = 1
100% it will happen!
4
4
Ex. 1b. If two are picked at random, what is the probability they lie on ray CA?
AB
C
D
Order possibilities!
AB BC CD
AC BD
AD
Remember AB is the same as BA
Circle winners.
P =
= or 1:2 or 50%
3
6
1
2
Ex. 2 What is the probability of picking Point Q on AC and it be within 5 units of B?
A CB
-20 7 10
Find the probability by comparing the length of the “winning” region
Total numbers between -20 and 10 = 30
Within 5 units of B = 8
P = winnerspossibilities
=
=
8
30
4
15