Probability – 1.6

Write each number as a percent.

1. 2. 1

3. 0.0043 4.

5. 1.04 6. 3

Probability – Warm Up38

56

1 400

1. = 3 ÷ 8 = 0.375 = 0.375(100%) = 37.5%

2. 1 = = 11 ÷ 6 = 1.83 = 1.83(100%) = 183 %

3. 0.0043 = 0.0043(100%) = 0.43%

4. = 1 ÷ 400 = 0.0025 = 0.0025(100%) = 0.25%

5. 1.04 = 1.04(100%) = 104%

6. 3 = 3(100%) = 300%

Solutions

Probability – Warm Up

1 400

56

116

13

38

There are two types of Probability:

• Experimental probability –

P (event) = number of times the event occursnumber of trials

• Theoretical Probability –

P(A) = m n

m = number of favorable outcomesn = number of equally likely outcomes

ProbabilityA 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) = = 0.16, or 16% 8 50

ProbabilityFind 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.

26 6 equally likely outcomes are in

the sample space.

2 outcomes result in a multiple of 3.

13=

ProbabilityBrown 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?

B b

B BB Bb

b Bb bb

Gene fromFather

Gene fromMother

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}.

14

The outcome bb is the only one for which a child will have blue eyes. So,

P(blue eyes) = .

14The theoretical probability that the child will have blue eyes is , or 25%.

Geometry ProbabilityGeometric Probability =

area that would give a favorable solution

total area

R = 1

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

ProbabilityFor the dartboard above, find the probability that a dart that lands at

random on the dartboard hits the outer ring.

P(outer ring) = area of outer ring area of circle with radius 4r

= (area of circle with radius 4r) – (area of circle with radius 3r)area of circle with radius 4r

=16 r 2 – 9 r 2

16 r 2

=16 r 2

7 r 2

=(4r)2 – (3r)2

(4r2)

= 7 16

The theoretical probability of hitting the outer ring is , or

about 44%.

7 16

Radius = 1

Each ring has a width of 1

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)