A spinning wheel is divided into 56 equal sectors that are coloured either red or blue.
Chablis spins the wheel and has a 1 in 8 chance of landing in a sector coloured red.
How many blue sectors are there on the spinning wheel?
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A spinning wheel is divided into 56 equal sectors that are coloured either red or blue.
Chablis spins the wheel and has a 1 in 8 chance of landing in a sector coloured red.
How many blue sectors are there on the spinning wheel?
`49`
`text(Number of red sectors)`  `= 1/8 xx 56` 
`= 7` 
`text(Number of blue sectors)`  `=\ text(Total sectors – Red sectors)` 
`= 56  7`  
`= 49` 
Two fair dice were rolled and the numbers on each die were added up.
Which resulting sum is most likely to occur?

2 

9 

11 

12 
`9`
`text{Check each option:}`
`text{Sum of 2  (1, 1)}`
`text{Sum of 9  (3, 6), (6, 3), (4, 5), (5, 4)}`
`text{Sum of 11  (5, 6), (6, 5)}`
`text{Sum of 12  (6, 6)}`
`:. \ text{Sum of 9 is most likely.}`
Marie flips an unbiased coin for 126 times.
Which result is most likely?

38 heads 

52 heads 

60 heads 

79 tails 
`text{60 heads}`
`text{The expected result is 63 heads or tails (half of total).}`
`therefore \ text{Most likely result is 60 heads.}`
Aaron rolls a fair dice four times.
Each time he rolls the dice he gets a three.
Aaron rolls the dice for the fifth time.
Which of the following is true?

He is less likely to roll a two than a three. 

He is more likely to roll a three than a one. 

He has an equal chance of rolling a three as a six. 

He is certain to roll a three. 
`text(He has an equal chance of rolling a three as a six)`
`text(All numbers in a fair die have equal chance of appearing.)`
`:.\ text(He has an equal chance of rolling a three as a six.)`
A partial deck of cards consists of 8 diamonds, 9 clubs, 4 spades and 3 hearts.
Patrick draws a card from the deck without looking.
What is the probability that he draws a spade?

`1/4` 

`4/21` 

`1/3` 

`1/6` 
`1/6`
`P(text(Spade))`  `= text(Total Number of spades)/text(Total cards)` 
`= 4/(8 + 9 + 4 + 3)`  
`= 4/24`  
`= 1/6` 
Lester schedules a company meeting twice every 5 working days.
Today is a working day.
What is the probability that there is a meeting scheduled?

`2/7` 

`0.40` 

`3/5` 

`text(25%)` 
`0.40`
`P`  `= text(Favorable Events)/text(Total Possible Events)` 
`= 2/5`  
`= 0.40` 
Andrei has a stack of cards that contains only Aces, Kings, Queens, Jacks and Jokers.
He picks one card without looking, records the card and puts it back again with the others.
He repeated this process 62 times.
Using the table, what are the chances of Andrei randomly selecting the Joker in his next pick?

`8/33` 

`6/31` 

`11/62` 

`6/25` 
`6/31`
`P(text(Joker))`  `= text(Number of Jokers)/text(Total number of draws)` 
`= 12/62`  
`= 6/31` 
A bookmaker's bag is filled with different types of notes.
The bag contains 16 tendollar notes, 11 twentydollar notes, 8 fiftydollar notes and 3 hundreddollar notes.
The bookmaker reaches in to the bag and randomly selects one note.
What is the chance that a fiftydollar note is selected?

`4/19` 

`8/29` 

`6/17` 

`4/17` 
`4/19`
`P(text($50 bill))`  `= text(Number of $50 bills)/text(Total number of bills)` 
`= 8/(16 + 11 + 8 + 3)`  
`= 8/38`  
`= 4/19` 
An AFL coach gave a press conference where she stated it was likely that her star player would return from injury for the next game.
Which probability below best describes the chance of the star player returning from injury?

`0.3`  

`1/2`  

`7/10`  

`9.5` 
`7/10`
`text{Probability of "likely" is between 0.5 and 1.}`
`text{(probability cannot be > 1)}`
`therefore \ frac{7}{10}`
A bag contains 10 coloured balls.
William took 4 balls out of the bag at the same time.
Which of the following results is impossible?

2 striped balls, one purple and one green ball. 

2 striped balls, one purple and one black ball. 

2 black balls and 2 striped balls. 

2 red balls and 2 black balls. 
`text(2 blue balls and 2 black balls.)`
`text(2 red balls and 2 black balls since there is only one red ball)`
`text{in the bag.}`
A bag contains 10 coloured marbles.
Sarah picks 3 marbles out of the bag at the same time.
Which of the following results is impossible?

3 pink marbles. 

2 red marbles and 1 green marble. 

2 blue marbles and 1 green marble. 

3 red marbles. 
`text(3 red marbles.)`
`text(3 red marbles since there is only 2 red marbles)`
`text{in the bag}`
There are 10 balls in a box numbered from 1 to 10.
The probability of choosing a number higher than 6 is 40%.
What is the probability to get a number less than or equal to 6?
% 
`text(60%)`
`Ptext{(less than or equal to 6)}`
`= 1  Ptext{(higher than 6)}`  
`= 1  0.40`  
`= 0.60`  
`= 60 text(%)` 
A dice in the shape of a rectangular prism has 6 faces numbered 1 to 6.
Jevin throws the dice 100 times and and records the outcomes.
What is the probability of throwing a 2 with this dice?
`12/31`  `11/50`  `3/8`  `9/17` 




`11/50`
`P(2)`  `=22/100` 
`=11/50` 
A rectangular prism die has 6 faces with faces numbered with 1 to 6 dots.
Dave throws the die 100 times and records the outcomes.
What is the probability of throwing a 5 with this die?
`1/4`  `2/7`  `3/25`  `15/26` 




`3/25`
`P(5)`  `=12/100` 
`=3/25` 
A professional darts player throws darts at a circular board that is divided into 4 sections.
He records which section he hits each time and the results are summarised in the table below.
Based on Robert’s data, what is the probability that his next throw will land in section 2 or 3?
Express your answer as a percentage rounded to the nearest tenth.
% 
`text(33.8%)`
`text(Number of throws)`  `= 26 + 14 + 13 + 27` 
`= 80` 
`:.\ text(Probability)`  `= (14 + 13)/80` 
`= 27/80`  
`= 0.3375`  
`~~ 33.8text(%)` 
Robert throws darts at a circular board that is divided into 4 sections.
He records which section he hits each time and the results are summarised in the table below.
Based on Robert’s data, what is the probability that his next throw will land in section 1 or 2?
Express your answer as a percentage rounded to the nearest tenth.
% 
`text(48.6%)`
`text(Number of throws)`  `= 4 + 30 + 26 + 10` 
`= 70` 
`:.\ text(Probability)`  `= (4 + 30)/70` 
`= 34/70`  
`= 0.4857`  
`~~ 48.6text(%)` 
Jevin tossed a coin 40 times.
He wrote down if the result was a head or tail each time, and recorded the results in the table below.
What is the difference between the expected number of tails and the actual number recorded?
`3`
`text(Probability of tails) = 1/2`
`text(Expected number of tails)`
`= 1/2 xx 40`
`= 20`
`:.\ text(Difference)`  `= 20  17` 
`= 3` 
Penelope has a bag of jelly beans.
The jelly beans are flavoured vanilla, raspberry and licorice.
Penelope picks one jelly bean from her bag.
Which of the following could be the probability that the jelly bean she picks is vanilla.
`3/17`  `1.02`  `0`  `19/3` 




`3/17`
`text(Any probability must be between 0 and 1.)`
`text(Probability cannot be equal to zero because we're)`
`text(told there are vanilla jelly beans in the bag.)`
`:.\ text(Only possibility is)\ \ 3/17`
Tuxedo tosses a coin 5 times and it lands on heads each time.
If he tosses the coin a 6th time, the most likely result is:

a head 

a tail 

both heads and tails have the same chance 
`text(both heads and tails have the same chance)`
`text(A coin toss has the same chance)`
`text(of a head or tail each time.)`
Bryant rolled a standard dice 70 times.
He recorded if an odd or even number was rolled, each time, and wrote the results in the table below.
What is the difference between the expected number of even rolls and the actual number recorded?
`4`
`text(Probability of even number) = 3/6 = 50text(%)`
`=>\ text(Expected even number rolls)`
`= 50text(%) xx 70`
`= 35`
`:.\ text(Difference)`  `= 39  35` 
`= 4` 
A survey of 300 Year 10 students asked what brand of phone they owned.
The results are shown in the table below.
One of these students is chosen at random.
What is the probability that the student owns a Nokia phone?
`0.1`  `0.2`  `0.3`  `0.6` 




`0.1`
`text{Pr(owning a Nokia phone)}`
`=30/300`
`= 0.1`
Manuel chooses a positive whole number under 5 and Basil has to guess what number it is.
The probability that Basil chooses the right number is 25%.
What is the probability that Basil chooses the wrong whole number?
% 
`text(75%)`
`text{Pr(Basil chooses the wrong number)}`
`= 1  text{Pr(right number)}`
`= 1  0.25`
`= 0.75`
`= 75 text(%)`
Keenak spins the arrow on a chocolate wheel to win an amount of money.
The arrow has an equal chance of landing on each section.
What is the probability that Keenak will win more than $50?
`0.125`  `0.15`  `0.25`  `0.375`  `0.625` 





`0.375`
`Pr (> $50)`  `= text(sections > $50)/text(total possibilities)` 
`= 3/8`  
`= 0.375` 
Emma works Monday till Friday. She gets the bus to work 4 days per week and catches the ferry on the other day.
Today is a work day.
What is the probability that Emma catches the ferry to work?
`0.25`  `1/7`  `5/7`  `text(20%)` 




`text(20%)`
`text(Probability)`  `= 1/5` 
`= 0.20`  
`= 20 text(%)` 