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1-6 Probability
Hubarth
Algebra II
Definition
Experimental Probability
Experimental probability of event = P(event)
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
Ex. 1 Finding Experimental probability
A player hit the bull’s eye on a circular dartboard 8 times out of 50. Find
the experimental probability that the player hits the bull’s eye.
P(bull’s eye) = 8 = 0.16, or 16%
50
Ex. 2 Using a Simulation
Describe a simulation you could use that involves flipping a coin to find
the experimental probability of guessing exactly 2 answers out of 6
correctly on a true-false quiz.
Getting heads with a flip of a coin has the same probability as guessing
the correct answer to a question on a true-false test.
So, let heads represent a correct answer and tails represent an incorrect
answer.
To simulate guessing the answers for a six-question true-false test, flip a
coin six times. Record the number of heads.
Repeat 100 times.
Count to see how many times heads came up exactly twice.
Divide this number by 100.
The result is the experimental probability that the simulation gives for
guessing 2 correct answers out of 6.
Ex. 3 Finding Theoretical Probability
Find the theoretical probability of rolling a multiple of 3 with a number
cube.
To roll a multiple of 3 with a number cube, you must roll 3 or 6.
2 outcomes result in a
multiple of 3.
2
6
1
=3
6 equally likely outcomes are in
the sample space.
Ex. 4 Real-World Connection
Brown is a dominant eye color for human beings. If a father and
mother each carry a gene for brown eyes and a gene for blue eyes,
what is the probability of their having a child with blue eyes?
Gene from
Father
B
b
Gene from
Mother
B
b
BB
Bb
Bb
bb
Let B represent the dominant gene for brown eyes. Let b represent the
recessive gene for blue eyes.
The sample space contains four equally likely outcomes {BB, Bb, Bb, bb}.
The outcome bb is the only one for which a child will have blue eyes. So,
1
P(blue eyes) = 4 .
1
The theoretical probability that the child will have blue eyes is 4 , or 25%.
The width of each
ring is r
Ex. 5 Finding Geometric Probability
Suppose all the circular dartboard shown at the right are equally
likely to be hit by a dart you have thrown. Find the probability of
Scoring at least ten points.
P(at least 10 points)
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠 2𝑟
=
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠 4𝑟
𝜋(2𝑟)2
=
𝜋(4𝑟)2
4𝜋𝑟 2
=
16𝜋𝑟 2
=
1
4
2
5
10
.
20
Practice
1. In the 2006 Rose Bowl, USC’s quarterback completed 29 of 40 passes. Find the
experimental probability.
29
= 0.725, 𝑜𝑟 72.5%
40
2. Find the theoretical probability of getting a prime number when you roll a number cube.
1
, 𝑜𝑟 50%
2
3. Using the information in example 4, what is the theoretical probability of a child having
brown eyes.
Gene from
1
, 𝑜𝑟 25%
4
Gene from
Father
4. Using the dartboard from example 5, Find each probability.
a. P(scoring 20 points)
b. P(scoring 5 points)
1
, 𝑜𝑟 6.25%
16
5
, 𝑜𝑟 31.25%
16
B
B
Mother
B
b
BBB
Bb
Bb
bb