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6.16. The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events. . Vocabulary 6.16 (handout) pg Vocabulary 6.16 Sample space - The set of all possible outcomes in a probability experiment.

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### 6.16

The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events.

Vocabulary 6.16 (handout)pg

Vocabulary 6.16

Sample space - The set of all possible outcomes in a probability experiment.

Probability – The chance of an event occurring; expressed using a ratio. The numerator describes how many times the event will occur, while the denominator describes the total number of outcomes for the event.

Outcome- Possible results of a probability event. For example, 4 is an outcome when a number cube is rolled.

Ratio- A comparison of two numbers by division. Example: The ratio 2 to 3 can be expressed as 2 out of 3, 2:3, or 2/3.

Event–A specific outcome or type of outcome.

Possible Outcome –all the possible events in a probability experiment

Simple Probability- One event occurring in a probability experiment

Independent Events - When one event is not affected by a second event

Spin two spinners. One has yellow, green, and blue. The other has only orange and purple. The probability of landing on yellow on the first spinner (1/3) and purple on the second is (½) …so……………

1/3 • ½= 1/6

Dependent Events - The result of one event affects the result of a second event.

There are six cookies. 2 are oatmeal, 3 are peanut butter, and 1 is sugar.

Probability of choosing a peanut butter is 3/6. THEN choosing an oatmeal is 2/5 (because you took a cookie out). Multiply them and you have the probability of choosing a peanut butter and then an oatmeal cookie!

3/6 • 2/5 = 6/30 and simplified is 1/5…so a 20% chance

*The probability of an event occurring is a ratio between 0 and 1.

– A probability of 0 means the event will never occur. Example like 0/8 means if you have 4 black, 2 blue, and 2 red socks, the probability of choosing yellow is 0/8 or 0.

– A probability of 1 means the event will always occur. Example 5 out of 5 ( 5/5) chance means 1….like all blue socks to choose from.

Probability can be expressed as a fraction, decimal, or percent.

0 25% 50% 75% 100%

Complete the number line with CERTAIN (100%), LIKELY (>50%), UNLIKELY (<50%), IMPOSSIBLE (0%) or use the chart on page 452 in book and graphing probability on a number line from 0-1 with specific examples.

Pg Practice 6.16

Simple Probability

There are 4 blue socks, 2 yellow socks, 6 red socks, and

2 green socks in a drawer.

Make a representation of the data

B BBB Y Y R RRRRR G G

What is the probability of choosing a green sock?

What is the probability of choosing a white sock?

Independent Events

Probability of rolling a 6 on one number cube and a

3 or a 5 on the other?

Make a representation of the data

1 2 3 4 5 6 1 2 3 4 5 6

X ==

Dependent Events

Probability of choosing a blue marble and then a green marble.

DON’T FORGET TO SUBTRACT OUT THE MARBLE YOU REMOVED!

Make a representation of the data

B BB Y R R G GB BB Y R R G G

X = =

Pg 6.16 Independent Events

Nothing is taken away

Probability of rolling two number cubes and getting snake eyes (or any doubles for that matter)?

There is a 1 in 6 chance for cube A and a 1 in 6 chance for cube B.

• =

Probability of spinning a blue on Spinner A and spinning a red on Spinner B?

Spinner A Spinner B F D P

Probability of tossing a heads on the coin and spinning a green or blue on the spinner?

F D P

6.16 Dependent Events Pg

Something is taken away

These are a little tricky!

Probability of choosing a red lollipop and then choosing a yellow lollipop?

First, there are 7 lollipops. Choosing a red has a probability.

Next, since you took one out there are only six left, so the probability of choosing a yellow is

R

(1/7)(1/6) = 1/42

O Y

B Pink F D P

G D B

What is the probability of choosing a Reeses and then choosing a Kit Kat?

F D P

Y

B

G

R

Y

B

G

R