Transcript Section 4 * 5 Applying Ratios to Probability

Section 4 – 5
Applying Ratios to
Probability
Objectives:
To find theoretical probability
To find experimental probability
Probability of an Event: P(event)
Tells you how likely it is that something
will occur
Event:
Any outcome or group of outcomes
Same Space:
All of the possible outcomes
Outcome:
The result of a single trial, like one roll of a
number cube
Example: P(rolling an even number)
Event: Rolling an even number on a
number cube.
Sample Space (possible outcomes):
1, 2, 3, 4, 5, 6
Favorable Outcome: 2, 4, 6
When all possible outcomes are
equally likely to occur, you can find
the theoretical probability using the
following formula:
Theoretical Probability:
P(event) =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
The probability of an event can be
written as a fraction, decimal or
percent.
Example 1 Finding
Theoretical Probability
A)
What is the probability of flipping a coin
and getting a tail.
B)
What is the probability of rolling a 1 or
6 on a die?
C)
What is the probability of spinning purple?
D)
What is the probability of spinning white or
green?
E)
A bowl contains 12 slips of paper, each with a
different name of a month. Find the theoretical
probability that a slip selected from the bowl has a
name of a month that starts with the letter J.
F)
Suppose you write the names of days of the
week on identical pieces of paper. Find the theoretical
probability of picking a piece of paper at random that
has the name of a day that starts with the letter T.
Complement of an event:
All of the outcomes NOT in the event.
The probability of an event and its complement add up to 1!
C)
What is the probability of spinning purple?
D)
What is the probability of NOT
spinning
spinning
whitepurple?
or
green?
Example 2 Finding the
Complement of an Event
A) Find the probability of NOT flipping a coin and getting
a tail.
B)
What is the probability of NOT rolling a 1 or 6 on
a die?
C)
On a popular television game show, a
contestant must choose one of five envelopes. One
envelope contains the grand prize, a car. Find the
probability of NOT choosing the car.
D)
You decide to buy 50/50 tickets at the football
game on Saturday. If 50 people buy 10 tickets each,
what is the probability that they will not pick your
ticket?
What happens to the P(not picking your ticket) if the number
of tickets bought increases?
Experimental Probability:
Probability based on data collected from
repeated trials.
Experimental Probability:
P(event) =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑡ℎ𝑒 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡 𝑖𝑠 𝑑𝑜𝑛𝑒
How Does Experimental Probability &
Theoretical Probability Compare?
The more times an experiment is done, the closer the
experimental probability gets to the theoretical
probability. We call this the Law of Large Numbers.
Example 3
Finding
Experimental Probability
A)
After receiving complaints, a skateboard
manufacturer inspected 1000 skateboarders at
random. The manufacturer found no defects in 992
skateboards. What is the probability that a skateboard
selected at random had no defect?
B)
The skateboard manufacturer decides to
inspect 2500 skateboards. There are 2450
skateboards that have no defects. Find the probability
that a skateboard selected at random has no defects.
Example 4
Using
Experimental Probability
A)
A manufacturer has 8976 skateboards in its
warehouse. If the probability that a skateboard
has no defect is 99.2%, predict how many
skateboards are likely to have no defect.
B)
A manufacturer has 8976 skateboards in its
warehouse. If the probability that a skateboard
has no defect is 81%, predict how many
skateboards are likely to have defects.