Tawa College - Yr 10 Probability Revision

Yr 10 Probability Revision

By L MacEwan

We can ​use different methods to find the sample space of a coin and a dice

List

{H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

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Table

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1. Sample Space​ ( all possible outcomes of an event)

​	​	​	​	Dice	​	​	​
​	​	​1	2​	3​	4​	5​	6​
​Coin	​H	​1H	​2H	​3H	​4H	​5H	​6H
​	​T	​1T	​2T	​3T	​4T	​5T	​6T

​Tree

Multiple Choice

Which shows the sample space for flipping two coins? 
H = heads, T = tails

• H, T
• HH, HT, TH, TT
• HH, TT
• HH, TT, TT, HH

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

What is the sample space?

• 6 bears

• orange, green, red, white, yellow

• unlikely

• 2 red bears

Fill in the Blanks

Equally likely outcomes

Multiple Choice

Describe the likelihood of an event with the probability of 1.

• certain to happen

• impossible to happen

• unlikely to happen

• equally likely as not to happen

Multiple Choice

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles.

P(A marble is purple)

• 5/10

• 1/3
• 5/9

• 3/10

Multiple Choice

An experiment consists of spinning the spinner once. Find the probability of landing on a 2.

• $$\frac{2}{8}$$

• $$\frac{1}{8}$$

• $$\frac{3}{8}$$

• $$\frac{8}{8}$$

• $$\frac{5}{8}$$

Multiple Choice

An experiment consists of randomly picking a square section for the 16-space board shown. Find the probability of choosing a triangle.

• $$\frac{1}{2}$$  

• $$\frac{8}{12}$$  

• $$\frac{8}{10}$$  

• $$\frac{4}{16}$$  

• $$\frac{12}{16}$$  

Multiple Choice

What is the probability that the spinner lands on a section labeled "Win"?

• $$\frac{2}{8}$$  

• $$\frac{2}{7}$$  

• $$\frac{1}{6}$$  

• $$\frac{2}{2}$$  

Multiple Choice

What is the P(greater than 2)?

• $$\frac{3}{4}$$

• $$\frac{7}{8}$$

• $$\frac{5}{8}$$

• $$\frac{1}{2}$$

• $$\frac{6}{7}$$

Probability with Tables

​When given a table for probability we add up all the rows and columns to get totals first.

The two way table shows the distribution of yr 7 and 11 preferences for icecream. 

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​When answering questions using this table, we need to use the total applicable on the bottom

e.g. Prob(yr 11 and Vanilla) is 11/82

e.g Prob( a yr 11 likes Vanilla)​ is 11/42

because it is only year 11 and not year 9​

Multiple Choice

The table shows the numbers of boys and girls that are enrolled in Spanish, French, or German class. If a student is chosen at random, what is the probability that the student is in Spanish and is a boy?

• $$\frac{45}{50}$$  

• $$\frac{10}{25}$$  

• $$\frac{10}{50}$$  

• $$\frac{25}{50}$$  

Multiple Choice

60 Students were surveyed about their favorite sport. What is the probability a student picked at random will like Basketball?

• $$\frac{15}{60}$$  

• $$\frac{26}{60}$$  

• $$\frac{8}{15}$$  

• $$\frac{9}{10}$$  

Multiple Choice

Students were surveyed about their favorite sport

What is the probability a 7th grade student picked at random will like Football?

• $$\frac{10}{18}$$  

• $$\frac{10}{20}$$  

• $$\frac{8}{12}$$  

• $$\frac{10}{60}$$  

Fill in the Blanks

Multiple Choice

The Bargain Auto Mall has these cars in stock.  If a car is selected at random, find the probability that it is Foreign and mid-sized.

• 20/300
• 135/300
• 155/300
• 40/300

Multiple Choice

The Bargain Auto Mall has these cars in stock.  If a car is selected at random, find the probability that it is Domestic or an SUV.

• 210/300
• 85/300
• 295/300
• 230/300

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​Probability Trees

Probability Trees help us when we are combining EVENTS

• Each vertical set of branches is an event e.g Name and answer

• ​each single set of branches adds to 1

• we multiply across ​branches

​Sample Space

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​Sam Yes

​Sam No

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​Alex Yes

Alex No​

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​ Name Answer

​e.g. Sam is 60% more likely to be rung for an extra shift at McD's

It is 50-50 whether Sam will say yes but Alex says No 70% of the

time​

​What is the probability of Sam being asked and saying Yes? 0.3

What is the probability of someone saying yes? 0.3 +0.12 = 0.42​

Multiple Choice

Find the probability of picking two blue pens

• $$\frac{56}{90}$$

• $$\frac{16}{90}$$

• $$\frac{64}{100}$$

• $$\frac{15}{90}$$

Multiple Choice

The probability tree shows the outcomes of flipping a coin twice.

What is the probability the coin lands on heads twice?

• 0.5

• 0.1

• 0.25

• 1

Multiple Choice

Find the probability of selecting two lemon sweets

• $$\frac{10}{18}$$

• $$\frac{25}{81}$$

• $$\frac{16}{81}$$

• $$\frac{20}{81}$$

Multiple Choice

What is the probability the dessert has peanut butter in it?

• 0.84

• 0.58

• 0.22

• 0.59

Multiple Choice

What is the probability that the dessert doesn't have peanut butter in it?

• 1.16

• 0.41

• 0.38

• 0.78

Multiple Choice

Here is a partially completed probability tree showing the probability of winning on a Teddy Grabber and a Penny Drop.

What is the probability of losing both games?

• $$\frac{6}{15}$$

• $$\frac{3}{5}$$

• $$\frac{3}{15}$$

• None of these

Multiple Choice

What is the probability of winning exactly one game?

• $$\frac{3}{15}$$

• $$\frac{13}{15}$$

• $$\frac{7}{15}$$

• None of these

​Expected Number

Multiple Choice

A fair, 6-sided dice is thrown 120 times.

Roughly how many times would you expect the number 5 to come up?

• 6

• 10

• 12

• 20

Multiple Choice

Raz’s pencil case contains 3 red, 2 blue and 5 black pens.

He takes a pen out without looking then puts it back 100 times.

Roughly how many times would you expect him to pick up a red pen?

• 10

• 20

• 30

• 50

Multiple Choice

A box contains 12 red, 20 green and 8 yellow sweets.

One is picked out at random then placed back 80 times.

Roughly how many times would you expect him to pick up a yellow sweet?

• 8

• 12

• 16

• 24

Multiple Choice

A spinner has 5 sections with the following numbers on it:

3 4 4 5 6

Each section is equally likely.

It is spun 75 times.

Roughly how many times would you expect him the spinner to land on 4?

• 5

• 15

• 25

• 30

Multiple Choice

The probability that it will rain for the next 2 weeks is 5/7.

Roughly how many days would you expect it to rain in the next 2 weeks?

• 2

• 4

• 5

• 10

​A fair game

Multiple Choice

The spinner is spun. Determine if the game is fair. If it is not fair, who has the greater probability of winning?

You win if the number is greater than 5. Your friend wins if the number is 5 or less.

• Not fair; Friend has a greater probability of winning

• Not fair; You have a greater probability of winning

• The game is fair

• Not fair; Unable to tell who has a greater probability of winning

Multiple Choice

Hadlee and Liam are playing with playing cards. They decide to shuffle a deck of playing cards. After a shuffle they choose a single card. If that card is of an Ace or a King they win 2 points. If that card is of a Jack or a Queen they win 3 points. If that card is of any other number, they lose 1 point. Is this game fair?

• Fair

• Not fair

Multiple Choice

Georgia and Olivia are the two baseball captains. They roll a die and decide that if the die lands with an even number, Eliza’s team will bat first. Otherwise Alisha’s team will bat first. Is this method fair?

• Fair

• Not fair

Multiple Choice

Synclair and his cousins are rolling dice. They decide that if they roll a 1 or 2 then they will win 3 points. If the number is 3 or 4 then they win 4 points. If they roll a 5 or 6 they win 5 points. Is this game fair?

• Fair

• Not fair

Multiple Choice

Sophia and Ava are playing with dice. They roll one die. If the die lands on the number 2 then they win 7 candies. If the die lands on the number 5 then they win one candy. If the die lands on any other number, they lose 2 candies. Is this game fair?

• Fair

• Not fair