Yr 9 Probability Review

Probability Review

Probability Part 1

Key Terms

• A random experiment will result in a list of outcomes without interference

• A sample space is a list of all possible outcomes in an experiment, and are listed using set brackets {...}

• An event can be a single outcome or a collection of outcomes. E.g. rolling a 1, or rolling an even number

• A compound event is an event that contains more than one outcome from the sample space. E.g. rolling an even number

Key Terms

• The formula to find the probability for an event where all outcomes are equally likely is:  $\Pr\left(event\right)=\frac{Number\ of\ outcomes\ where\ event\ occurs}{Total\ number\ of\ outcomes}$ 

• Probabilities are represented by values from 0 to 1, with 0 as impossible and 1 as certain. They can be written as fractions, decimals and percentages. E.g.  $\frac{1}{4}=0.25=25\%$  

• So for all events,  $0\le\Pr\left(event\right)\le1$  

Key Terms

• The probability of event  $A$ , is written as  $\Pr\left(A\right)$ 

• The event in which  $A$  does not occur is referred to as the complement of  $A$ . This is also known as  $\Pr\left(not\ A\right)$  or  $\Pr\left(A'\right)$ 

•  $\Pr\left(A\right)=1-\Pr\left(A'\right)$  

• This also means  $\Pr\left(A'\right)=1-\Pr\left(A\right)$  and  $1=\Pr\left(A\right)+\Pr\left(A'\right)$  

Example 1

• The sample space for the spinner is  $\left\{1,\ 2,\ 3,\ 7\right\}$ 

• The probability of landing on 3 is $\Pr\left(3\right)=\frac{2}{5}$ 

• The probability of landing on a number that is not 3 is $\Pr\left(not\ 3\right)=\frac{3}{5}$ 

Fill in the Blanks

Multiple Choice

What is the probability of landing on a 2?

Find  $\Pr\left(2\right)$ 

•  $\frac{1}{5}$  

•  $\frac{6}{24}$  

•  $\frac{3}{8}$  

•  $\frac{1}{4}$  

Multiple Choice

What is the probability of not getting 2?

Find  $\Pr\left(not\ 2\right)$ 

•  $\frac{4}{5}$  

•  $\frac{18}{24}$  

•  $\frac{5}{8}$  

•  $\frac{3}{4}$  

Example 1

• The probability of landing on a 3 or 7 is $\Pr\left(a\ 3\ or\ a\ 7\right)=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$  

• The probability of landing on a number that is at least 2 (i.e. 2, 3, or 7) is  $\Pr\left(at\ least\ 2\right)=\frac{4}{5}$ 

Multiple Choice

What is the probability of getting a 3 or a 5?

Find  $\Pr\left(3\ or\ 5\right)$ 

•  $\frac{13}{24}$  

•  $\frac{2}{5}$  

•  $\frac{3}{8}$  

Multiple Select

What is the probability of getting a number that is at least a 3?

Find  $\Pr\left(at\ least\ 3\right)$ 

•  $\frac{3}{5}$  

•  $\frac{4}{8}$  

•  $\frac{17}{24}$  

•  $\frac{1}{2}$  

Example 2

• A random letter from the word PROBABILITY is chosen

• The sample space is  $\left\{P,\ R,\ O,\ B,\ A,\ I,\ L,\ T,\ Y\right\}$ 
  

• The probability of choosing L is  $\Pr\left(L\right)=\frac{1}{11}$  

• The probability of not choosing L is  $\Pr\left(not\ L\right)=\frac{10}{11}$  

• The probability of choosing B is  $\Pr\left(B\right)=\frac{2}{11}$  

Multiple Choice

A random letter from the word OCEANIA is chosen. 

Find  $\Pr\left(A\right)$ 

•  $\frac{2}{7}$  

•  $\frac{2}{6}$  

•  $\frac{1}{3}$  

Multiple Choice

A random letter from the word OCEANIA is chosen.
Find  $\Pr\left(not\ A\right)$  

•  $\frac{5}{7}$  

•  $\frac{5}{6}$  

•  $\frac{2}{3}$  

•  $\frac{4}{7}$  

Example 2

• A random letter from the word PROBABILITY is chosen

• The probability of choosing a vowel is  $\Pr\left(vowel\right)=\frac{4}{11}$  

• The probability of choosing a consonant is  $\Pr\left(consonant\right)=\frac{7}{11}$  

Multiple Choice

A random letter from the word OCEANIA is chosen. 

Find  $\Pr\left(vowel\right)$ 

•  $\frac{4}{6}$  

•  $\frac{4}{7}$  

•  $\frac{5}{7}$  

•  $\frac{2}{3}$  

Multiple Choice

A random letter from the word OCEANIA is chosen. 

Find $\Pr\left(consonant\right)$ 

•  $\frac{3}{6}$  

•  $\frac{3}{7}$  

•  $\frac{1}{2}$  

Example 2

• A random letter is chosen from the word PROBABILITY

• The probability of choosing a vowel or B is

   $\Pr\left(vowel\ or\ B\right)=\frac{4}{11}+\frac{2}{11}=\frac{6}{11}$ 
  

• There are only two types of letters in the alphabet: vowels and consonants

• The probability of choosing a vowel or consonant is  $\Pr\left(vowel\ or\ consonant\right)=\frac{4}{11}+\frac{7}{11}=1$  

Multiple Choice

A random letter from the word OCEANIA is chosen.
Find  $\Pr\left(consonant\ or\ A\right)$  

•  $\frac{5}{7}$  

•  $\frac{4}{6}$  

•  $\frac{2}{3}$  

•  $\frac{4}{7}$  

Poll

How do you feel about finding the probability of events?

• Confident!

• Good, I think I can do this

• Just okay, we'll see

• Need more practice

• Completely confused