Transcript Chapter 2-6: Probability

Probability - Simple Probability and Odds
1. Which measure of central
tendency best describes the data?
Explain.
Mean: 3.1, Median: 3.6, Mode:1.1
2.
78, 82, 85, 86, 87, 88, 88, 88, 89, 89, 90, 92, 95, 98, 98
WS 2-5 Practice #3, 4, 6 – 10 (7 problems – 17 points)
Probability - Simple Probability and Odds
One way to describe the likelihood of an event
occurring is with probability.
The probability of a simple event, like a coin landing
heads up when it is tossed, is a ratio of the number of
favorable outcomes for the event to the total number
of possible outcomes of the event.
The probability of an event can be expressed as a
fraction, a decimal, or a percent.
Probability - Simple Probability and Odds
Suppose you wanted to find the probability of rolling
a 4 on a die.
When you roll a die, there are six possible outcomes,
1, 2, 3, 4, 5 or 6.
This list of all possible outcomes is called the sample
space.
Of these outcomes, only one, a 4, is favorable.
So the probability of rolling a 4 is: 16 , 0.16 or about 17%
Probability - Simple Probability and Odds
REPEAT: The probability of a simple event is a ratio
of the number of favorable outcomes for the event to
the total number of possible outcomes of the event.
The probability of an event a can be expressed as:
number of favorable outcomes
Pa  
total number of possible outcomes
Find Probabilities of Simple Events
Find the probability of rolling a number greater
than 2 on a die.
There are six possible outcomes. Four of the outcomes
are favorable. That is, four of the six outcomes are
numbers greater than two.
4 numbers
greater than 2
Sample space: 1, 2, 3, 4, 5, 6
6 possible
outcomes
Answer:
Find Probabilities of Simple Events
A class contains 6 students with black hair, 8 with
brown hair, 4 with blonde hair, and 2 with red hair.
Find P(black).
There are 6 students with black hair and 20 total students.
number of favorable outcomes
number of possible outcomes
Simplify.
Answer: The probability of selecting a student with black
hair is
Find Probabilities of Simple Events
A class contains 6 students with black hair, 8 with
brown hair, 4 with blonde hair, and 2 with red hair.
Find P(red or brown).
There are 2 students with red hair and 8 students with
brown hair. So there are 2 + 8 or 10 students with red
or brown hair.
number of favorable outcomes
number of possible outcomes
Simplify.
Answer: The probability of selecting a student with red
or brown hair is
Find Probabilities of Simple Events
A class contains 6 students with black hair, 8 with
brown hair, 4 with blonde hair, and 2 with red hair.
Find P(not blonde).
There are 6 + 8 + 2 or 16 students who do not have
blonde hair.
number of favorable outcomes
number of possible outcomes
Simplify.
Answer: The probability of selecting a student who does
not have blonde hair is
Find Probabilities of Simple Events
a. Find the probability of rolling a
number less than 3 on a die.
Answer:
b. A gumball machine contains 40 red gumballs, 30
green gumballs, 50 yellows gumballs, and 40 blue
gumballs. Find P(red).
Answer:
Find Probabilities of Simple Events
c. A gumball machine contains 40 red gumballs, 30
green gumballs, 50 yellows gumballs, and 40 blue
gumballs. Find P(green or yellow).
Answer:
d. A gumball machine contains 40 red gumballs, 30
green gumballs, 50 yellows gumballs, and 40 blue
gumballs. Find P(not blue).
Answer:
Probability - Simple Probability and Odds
You should have noticed that the probability that an
event will occur is somewhere between 0 and 1 (or 0%
and 100%) inclusive.
If the probability of an event is 0, that means that it is
impossible for the event to occur.
A probability equal to 1 means that the event is certain to
occur.
There are outcomes for which the probability is ½.
When this happens, the outcomes are equally likely to
occur or not to occur.
Probability - Simple Probability and Odds
Probability - Simple Probability and Odds
Another way to express the chance of an event
occurring is with odds.
The odds of an event occurring is the ratio that
compares the number of ways an event can occur
(successes) to the number of ways it cannot occur
(failures).
ODDS
successes : failures
Odds of an Event
Find the odds of rolling a number greater than 2.
There are six possible outcomes, 4 are successes and
2 are failures.
4 numbers
greater than 2
4:2
Sample space: 1, 2, 3, 4, 5, 6
2 numbers
less than or
equal to 2
Answer: The odds of rolling a number greater than 2 are
4:2 or 2:1.
Odds of an Event
Find the odds of rolling a number less than 4.
Sample space: 1, 2, 3, 4, 5, 6
Answer: 3:3 or 1:1
Probability - Simple Probability and Odds
The odds AGAINST an event occurring are the odds
that the event will NOT occur.
Odds Against an Event
A card is selected at random from a standard
deck of 52 cards. What are the odds against
selecting a 2 or 3?
There are four 2s and four 3s in a deck of cards, and
there are 52 – 4 – 4 or 44 cards that are not a 2 or a 3.
number of ways not to pick
a 2 or 3
odds against a 2 or 3 = 44:8
number of ways to pick
a 2 or 3
Answer: The odds against selecting a 2 or 3 are 11:2.
Odds Against an Event
A card is selected at random from a standard
deck of 52 cards. What are the odds against
selecting a 5, 6, or 7?
Answer: 10:3
Probability and Odds
Travel Melvin is waiting to
board a flight to Washington,
D.C. According to the airline, the flight he is waiting for
is on time 80% of the times it flies. What are the odds
that the plane will be on time?
The probability that the plane will be on time is 80%, so
the probability that it will not be on time is 20%.
odds of the plane being on time
Answer: The odds that the plane will be on time are 4:1.
Probability and Odds
If the probability that it will snow this weekend is 70%,
what are the odds that it will snow?
Answer: 7:3