Transcript Probability - Skills Bridge

PROBABILITY
PROBABILITY
 Probability
is a measure of how likely an
event is to occur.
 For
example –
 Today there is a 60% chance of rain.
 The odds of winning the lottery are a
million to one.
 What are some examples you can think
of?
PROBABILITY
 Probabilities
are written as:

Fractions from 0 to 1

Decimals from 0 to 1

Percents from 0% to 100%
PROBABILITY
 If
an event is certain to happen, then the
probability of the event is 1 or 100%.
 If
an event will NEVER happen, then the
probability of the event is 0 or 0%.
 If
an event is just as likely to happen as to
not happen, then the probability of the
event is ½, 0.5 or 50%.
PROBABILITY
Impossible
Unlikely
Equal Chances
0
0.5
0%
50%
½
Likely
Certain
1
100%
VOCABULARY



Probability (P) – is the likelihood that an event
will occur.
Outcomes – when you do a probability
experiment the different possible results are
called outcomes
Event – is a collection of outcomes
TYPES OF PROBABILITY

There are 2 types of probability
Theoretical Probability
Experimental Probability

Let’s look at each one individually…
THEORETICAL PROBABILITY

Theoretical Probability is based upon the number
of favorable outcomes divided by the total
number of outcomes
Example:

In the roll of a die, the probability of getting an even
number is 3/6 or ½.
HOW DOES THAT WORK?

Each die contains the numbers 1, 2, 3, 4, 5, and 6.

Of those numbers only 2, 4, and 6 are even.

So, we can set up a ratio of the number of
favourable outcomes divided by the total number
of outcomes, which is 3/6 or 1/2
PROBABILITY



When a meteorologist states that the chance of
rain is 50%, the meteorologist is saying that it is
equally likely to rain or not to rain.
If the chance of rain rises to 80%, it is more likely
to rain.
If the chance drops to 20%, then it may rain, but
it probably will not rain.
PROBABILITY
 What
are some events that will never
happen and have a probability of 0%?
 What
are some events that are certain to
happen and have a probability of 100%?
 What
are some events that have equal
chances of happening and have a
probability of 50%?
PROBABILITY
 The
probability of an event is written:
P(event) = number of ways event can occur
total number of outcomes
PROBABILITY
P(event) = number of ways event can occur
total number of outcomes
 An
outcome is a possible result of a
probability experiment

When rolling a number cube, the possible
outcomes are 1, 2, 3, 4, 5, and 6
PROBABILITY
P(event) = number of ways event can occur
total number of outcomes
 An
event is a specific result of a
probability experiment

When rolling a number cube, the event of
rolling an even number is 3 (you could roll a
2, 4 or 6).
PROBABILITY
P(event) = number of ways event can occur
total number of outcomes
What is the probability of getting heads
when flipping a coin?
P(heads) = number of ways = 1 head on a coin = 1
total outcomes = 2 sides to a coin = 2
P(heads)= ½ = 0.5 = 50%
EXAMPLE # 1


A box contains 5 green pens, 3 blue pens, 8 black
pens and 4 red pens. A pen is picked at random
What is the probability that the pen is green?
There are 5 + 3 + 8 + 4 or 20 pens in the box
P (green) = # green pens
Total # of pens
= 5
20
=1
4
TRY THESE:
A
D
1. What is the probability that the spinner
will stop on part A?
1
2. What is the probability that the
spinner will stop on
(a) An even number?
(b) An odd number?
C B
3. What is the probability that the
spinner will stop in the area
marked A?
B
C
3
2
A
PROBABILITY WORD PROBLEM:

Lawrence is the captain of his track team. The
team is deciding on a color and all eight members
wrote their choice down on equal size cards. If
Lawrence picks one card at random, what is the
probability that he will pick blue?
Number of blues = 3
Total cards = 8
3/8 or 0.375 or 37.5%
blue
blue
yellow
red
green
black
blue
black
LET’S WORK THESE TOGETHER

Donald is rolling a number cube labeled 1 to 6.
What is the probability of the following?
a.) an odd number
odd numbers – 1, 3, 5
3/6 = ½ = 0.5 = 50%
total numbers – 1, 2, 3, 4, 5, 6
b.) a number greater than 5
numbers greater – 6
1/6 = 0.166 = 16.6%
total numbers – 1, 2, 3, 4, 5, 6
TRY THESE:
1
3
2
4
1. What is the probability of spinning a
number greater than 1?
2. What is the probability that a spinner
with five congruent sections numbered
1-5 will stop on an even number?
3. What is the probability of rolling a
multiple of 2 with one toss of a number
cube?
EXPERIMENTAL PROBABILITY

As the name suggests, Experimental Probability is
based upon repetitions of an actual experiment.
Example:
If you toss a coin 10 times and record that the number
of times the result was 8 heads, then the experimental
probability was 8/10 or 4/5
EXPERIMENTAL PROBABILITY FORMULA

Experimental Probability:
P=
Number of favorable outcomes
Total number trials
EXAMPLE #2

In an experiment a coin is tossed 15 times. The
recorded outcomes were: 6 heads and 9 tails.
What was the experimental probability of the
coin being heads?
P (heads) =
# Heads
Total # Tosses
=
6
15
ODDS
ODDS


Another way to describe the chance of an event
occurring is with odds. The odds in favor of an event
is the ratio that compares the number of ways the
event can occur to the number of ways the event
cannot occur.
We can determine odds using the following ratios:
Odds in Favor = number of successes
number of failures
Odds against =
number of failures
number of successes
EXAMPLE #3

Suppose we play a game with 2 number cubes.

If the sum of the numbers rolled is 6 or less – you win!

If the sum of the numbers rolled is not 6 or less – you lose
In this situation we can express odds as follows:
Odds in favor =
numbers rolled is 6 or less
numbers rolled is not 6 or less
Odds against =
`
numbers rolled is not 6 or less
numbers rolled is 6 or less
EXAMPLE #4

A bag contains 5 yellow marbles, 3 white marbles, and 1
black marble. What are the odds drawing a white marble
from the bag?
Odds in favor =
number of white marbles
number of non-white marbles
3
6
Odds against =
number of non-white marbles
number of white marbles
6
3
Therefore, the odds for are 1:2
and the odds against are 2:1
YOUR TURN - ODDS

5.
6.
7.
8.
Find the favorable odds of choosing the
indicated letter from a bag that contains the
letters in the name of the given state.
S; Mississippi
N; Pennsylvania
A; Nebraska
G; Virginia
YOUR TURN

You toss a six-sided number cube 20 times. For
twelve of the tosses the number tossed was 3 or
more.
9.
What is the experimental probability that the
number tossed was 3 or more?
10.
What are the odds in favour that the number
tossed was 3 or more?
YOUR TURN SOLUTIONS
5.
4/11
6.
7.
8.
9.
10.
¼
¼
1/8
3/5
3/2