Download 10/25 Probability Rules - School District of Clayton

FST 10/25/16
Probability Rules
Recall that
Name: ______________
, the union of sets A and B, contains all elements that are either in A or in B.
Recall that the intersection
of two sets A and B is the set of elements in both A and B.
If A and B have no elements in common, they are called
.
Addition Counting Principle (Mutually Exclusive Form)
If two finite sets A and B are mutually exclusive, then
=
Example:
Mr. Moody is planning an end of year party for some of his classes. If there are 19 students in Mr. Moody’s
1st hour, 9 students in Mr. Moody’s 4th hour, and 17 students in Mr. Moody’s 6th hour, how many bottles of
water should Mr. Moody purchase (assuming one bottle for each student)?
Theorem: Probability of the Union of Mutually Exclusive Events
If A and B are mutually exclusive events in the same finite sample space, then
=
Example:
If two dice are tossed, what is the probability of a sum of 7 or 11?
Addition Counting Principle (General Form)
For any finite sets A and B,
=
Example:
Mr. Moody is planning a Party with his three classes and Mrs. Lazaroff’s Biology Classes.
Mr. Moody has 45 students in his FST classes and Mrs. Lazaroff has 38 students in her Biology classes. They
would like to purchase enough bottles of water so that each student may have one bottle of water, how many
bottles of water should they purchase?
Before you answer the question above, what other information do you need to know?
Theorem (Probability of the Union of Events – General Form)
If A and B are any events in the same finite sample space, then
=
Example;
A pair of dice is thrown. What is the probability that the dice show doubles or a sum of 8?
Complementary Events:
Common notation:
Find P(sum of 2 dice is not greater than 9)
Independent events: Two events are independent if the occurrence of one event is not affected by the
occurrence of the second event.
Examples:
Probability:
Two events, A and B, are independent events if and only if
.
So this means:
Scenario: There are two 6-space spinners numbered #1-6. Each is spun once and there are two events defined
as:
A: The first spin stops on an even number.
B: The second spin stops on a multiple of three.
Are the two events independent?
A: The first spin stops on an even number.
B: The second spin results in a sum of the two values being 8.
Are the two events independent?
Problems to consider:
1.
The guide of an African Safari day trip stated that the probability of observing a cheetah on a given
day is 0.68, and the probability of observing a hyena is 0.52. The guide also stated that 40% of visitors
observe both a cheetah and a hyena on the same day. On this Safari trip, are observing a cheetah and
hyena independent events? Explain your reasoning.
2.
There are twelve old batteries in a junk box. Five (5) are completely dead, but you don't know which
ones. You start picking them out one at a time to test them and then put them on the table next to you.
What is the probability that at least one of the first three work?