Transcript 1.6 - Probability

Probability – 1.6
Probability – Warm Up
Write each number as a percent.
1. 38
2. 1 56
3. 0.0043
4.
5. 1.04
6. 3
1
400
Probability – Warm Up
Solutions
3
1. 8 = 3 ÷ 8 = 0.375 = 0.375(100%) = 37.5%
2. 1 5 = 11 = 11 ÷ 6 = 1.83 = 1.83(100%) = 183 1 %
6
6
3
3. 0.0043 = 0.0043(100%) = 0.43%
1
4. 400 = 1 ÷ 400 = 0.0025 = 0.0025(100%) = 0.25%
5. 1.04 = 1.04(100%) = 104%
6. 3 = 3(100%) = 300%
There are two types of Probability:
• Experimental probability –
P (event) = number of times the event occurs
number of trials
• Theoretical Probability –
P(A) = m
n
m = number of favorable outcomes
n = number of equally likely outcomes
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
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
6 equally likely outcomes are in
the sample space.
1
=3
Probability
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,
P(blue eyes) = 1 .
4
1
The theoretical probability that the child will have blue eyes is 4 , or 25%.
Geometry Probability
Geometric Probability =
area that would give a favorable solution
total area
Each ring has a
width of 1
How do we find
the probability of
hitting the purple
ring?
Strategy?? In your own
words, how would we
get the probability of
the purple ring
R=1
Probability
For the dartboard above, find the probability that a dart that lands at
random on the dartboard hits the outer ring.
of outer ring
P(outer ring) = area area
of circle with radius 4r
=
=
=
=
(area of circle with radius 4r) – (area of circle with radius 3r)
area of circle with radius 4r
(4r)2 – (3r)2
(4r2)
16
r2 – 9
16
7 r2
16
7
=
16
r2
r2
r2
Radius = 1
Each ring
has a width
of 1
The theoretical probability of hitting the outer ring is
about 44%.
7
, or
16
Random Number Generator
• When actual trials are difficult to conduct, you can find
experimental probabilities by using a simulation, which
is the model of one or more events.
• To create a random number list on the graphing
calculator, use the following keys:
MATH
RandInt
ENTER
Create a random number generator
for the integers 1 to 10
Input: (1, 10)