Intro to Probability

The list of all possible outcomes is called the SAMPLE SPACE.

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Probability is often defined as how likely something is to happen.

Multiple Choice

Sample space is defined as...

• the likelihood of an event occurring.

• a diagram of all possible outcomes.

• the probability of an event.

• a list of all possible outcomes.

Multiple Choice

The cafeteria is serving three kinds of sandwiches:  tuna (T), chicken, (C), and peanut butter (P).  They are also serving a choice of two drinks:  milk (M) or water (W).  Which shows the CORRECT Sample Space List of possible combinations?

• TW, CW, PW

• TW, TM, TC, CW, PW

• TW, TM, CW, CM, PW, PM

• TCP, MW

Multiple Choice

Which shows the sample space for flipping two coins?

• H, T

• HH, HT, TH, TT

• HH, TT

• Dime, Nickel

Multiple Choice

The tree diagram shows the sample space for picking an outfit from a choice of 3 shirts, 2 pants, and 2 shoes options. How many total outfit options are represented? (what is the total number in the sample space)

• 12

• 22

• 7

• 21

• 8

​We use ratios to show how likely, or unlikely, an outcome might be.  This ratio is called the probability of the event.  A probability is expressed as:

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Intuitive Idea of Probability

Multiple Choice

When figuring the probability of an event, what number goes on bottom of your fraction?

• The number of the desired event

• The total number of choices possible

• The event that happens most

• The event that happens least

Multiple Choice

When figuring the probability of an event, what number goes on top of your fraction?

• The number of the desired event

• The total number of choices possible

• The event that happens most

• The event that happens least

Multiple Choice

Find P(red marble)...

• 3/10

• 3/9

• 1/9

• 1/3

Multiple Choice

What is the probability of spinning the spinner and landing on a number greater than 6?

• $$\frac{3}{8}$$  

• 0

•   $$\frac{6}{8}=\frac{3}{4}$$  

• $$\frac{2}{8}=\frac{1}{4}$$

Multiple Choice

Find the probability of rolling greater than a 1 on a single die.

• 6/6

• 5/6

•   $$\frac{6}{8}=\frac{3}{4}$$  

• 1/6

Multiple Choice

A bag has 7 marbles: 2 green, 2 blue, and 3 orange. What is the probability of reaching in and NOT pulling out a green?

• 2/7

• 3/7

• 4/7

• 5/7

Multiple Choice

An event has a 0% chance of happening. This event is ___.

• Impossible

• Unlikely

• As likely as not

• Likely

• Certain

Multiple Choice

A bag has 7 marbles: 2 green, 2 blue, and 3 orange. What is the probability of reaching in and pulling out a red marble?

• 2/7

• 3/7

• 4/7

• 0

Multiple Choice

CHALLENGE: Given the image of the two squares, find the probability of a point being in the shaded area.

• $$\frac{4}{12}=\frac{1}{3}$$

• $$\frac{2}{6}=\frac{1}{3}$$

• $$\frac{4}{36}=\frac{1}{9}$$

• $$\frac{4}{32}=\frac{1}{8}$$

Multiple Choice

CHALLENGE: Given a point lands in the rectangle, find the probability of the point being in the shaded area.

• $$\frac{24}{36}=\frac{2}{3}$$

• $$\frac{36}{60}=\frac{3}{5}$$

• $$\frac{18}{60}=\frac{3}{10}$$

• $$\frac{18}{42}=\frac{3}{7}$$

• $$\frac{24}{60}=\frac{2}{5}$$

Venn diagrams can be used to express the logical (in the mathematical sense) relationships between various sets.

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The following Venn diagram shows a breakdown of a small high schools sports program.

​Venn Diagrams

Multiple Choice

The following Venn diagram shows a breakdown of a small high schools sports program. How many students play only Tennis?

• 14

• 21

• 18

• 7

Multiple Choice

The following Venn diagram shows a breakdown of a small high schools sports program. How many students play basketball and tennis?

• 10

• 13

• 7

• 5

Multiple Choice

The following Venn diagram shows a breakdown of a small high schools sports program. How many students that play a sport do not play basketball?

• 26

• 28

• 30

• 13

• 33

Multiple Choice

The following Venn diagram shows a breakdown of a small high schools sports program. How many students that play baseball or softball?

• 12

• 25

• 22

• 13

• 38

Multiple Choice

The following Venn diagram shows a breakdown of a small high schools sports program. How many students attend this school?

• 628

• 592

• 613

• 552

• not enough information