Simple Probability 1

Question 1 of 7

Given that the range of probability of an event happening is

$0\leq\mathsf{P(E)}\leq1$ , enter the equivalent probability for each keyword below:

$(i)$ Certain

$(ii)$ Even Chance

$(iii)$ Impossible

Write fractions in the format “a/b”

$(i)$ Certain $=$ (1, 1/1, 100/100)

$(ii)$ Even Chance $=$ (1/2, 0.5, 50/100)

$(iii)$ Impossible $=$ (0, 0/1, 0/100)

Incorrect

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Range of Probability

$0\leq\mathsf{P(E)}\leq1$

$(i)$ Find the equivalent probability of being certain that an event will happen.

This also means a

$100%$ chance for an event to happen, which is equivalent to the highest possible value for a probability

certain

$=1$

$(ii)$ Find the equivalent probability of having an even chance that an event will happen.

This also means

$50%$ chance for an even to happen. An example is tossing a coin since there is an even chance for Heads or Tails to show up.

even chance

$=1/2$ or

$0.5$

$(iii)$ Find the equivalent probability for an event to be impossible.

This also means a

$0%$ chance for an event to happen, which is equivalent to the lowest possible value for a probability

impossible

$=0$

$(i) 1$

$(ii) 1/2$ or

$0.5$

$(iii) 0$

Question 2 of 7

Find the probability of spinning the following spinners and getting:

$(i)$ Orange

$(ii)$ Pink

Write fractions in the format “a/b”

$(i)$ (1/2, 2/4, 0.5)

$(ii)$ (1/5, 0.2)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

$(i)$ Find the probability of getting Orange from the spinner.

favourable outcomes

$=$ $2$ (Orange)

total outcomes

$=$ $4$ (Orange, Blue, Orange, Yellow)

$\mathsf{P(Orange)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{2}}{\color{#007DDC}{4}}$	Substitute values

	$=$	$\frac{1}{2}$

$(ii)$ Find the probability of getting Pink from the spinner.

favourable outcomes

$=$ $1$ (Pink)

total outcomes

$=$ $5$ (Pink, Green, Orange, Blue, Yellow)

$\mathsf{P(Pink)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{1}}{\color{#007DDC}{5}}$	Substitute values

$(i) 1/2$

$(ii) 1/5$

Question 3 of 7

A spinning barrel holds

$100$ tickets for a raffle. Jake bought

$10$ of those tickets, Emma bought

$5$ , and Dylan bought

$1$ . Find the probability that:

$(c)$ Dylan will win

$(d)$ None of them will win

Write fractions in the format “a/b”

$(c)$ (1/100, 0.01)

$(d)$ (84/100, 21/25, 0.84)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

$(c)$ Find the probability that Dylan will win.

favourable outcomes

$=$ $1$ (Dylan bought

$1$ ticket)

total outcomes

$=$ $100$ (the barrel holds

$100$ tickets)

$\mathsf{P(Dylan)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{1}}{\color{#007DDC}{100}}$	Substitute values

$(d)$ Find the probability that none of them will win.

favourable outcomes

$=100-10-5-1=$ $84$ (tickets that were not bought by them)

total outcomes

$=$ $100$ (the barrel holds

$100$ tickets)

$\mathsf{P(none)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{84}}{\color{#007DDC}{100}}$	Substitute values

	$=$	$\frac{21}{25}$

$(c) 1/100$

$(d) 84/100$ or

$21/25$

Question 4 of 7

A spinning wheel has

$16$ sectors marked

$1$ -

$16$ . Each of these sectors corresponds to a ticket that can be bought and a lady named Jackie wants to buy some. Answer the following:

$(c)$ How many tickets should she buy to have a

$25%$ chance at winning?

$(d)$ What is the probability of her winning if she buys

$6$ tickets?

Write fractions in the format “a/b”

$(c)$ (4, 16/4) tickets

$(d)$ (3/8, 6/16, 0.375, 0.38)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

$(c)$ Find the number of tickets she should buy to have a

$25%$ chance at winning.

favourable outcomes

$=$ $x$ (number of tickets she should buy)

total outcomes

$=$ $16$ (the wheel has

$16$ sectors)

P(25%)

$=1/4$

$\mathsf{P(}25\%\mathsf{)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

$1/4$	$=$	$\frac{\color{#e65021}{x}}{\color{#007DDC}{16}}$	Substitute values

$1/4$ $times16$	$=$	$x/16$ $times16$	Multiple both sides by $16$

$4$	$=$	$x$
$x$	$=$	$4$

$(d)$ Find the probability of her winning if she buys

$6$ tickets.

favourable outcomes

$=$ $6$ (Jackie is about to buy

$6$ tickets)

total outcomes

$=$ $16$ (the wheel has

$16$ sectors)

$\mathsf{P(}6\mathsf{)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{6}}{\color{#007DDC}{16}}$	Substitute values

	$=$	$\frac{3}{8}$

$(c) 4$ tickets

$(d) 3/8$

Question 5 of 7

The numbers on this spinner correspond to the degree angle of that color. What is the probability of the arrow landing on:

$(a)$ Yellow

$(b)$ Blue

Write fractions in the format “a/b”

$(a)$ (1/2, 180/360, 0.5)

$(b)$ (1/9, 40/360, 0.11)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

$(a)$ Find the probability of the arrow landing on Yellow.

favourable outcomes

$=$ $180$ (degree measure of Yellow which is a semicircle)

total outcomes

$=$ $360$ (degree measure of the whole circle)

$\mathsf{P(Yellow)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{180}}{\color{#007DDC}{360}}$	Substitute values

	$=$	$\frac{1}{2}$

$(b)$ Find the probability of the arrow landing on Blue.

favourable outcomes

$=$ $40$ (Blue measures

$40$ degrees)

total outcomes

$=$ $360$ (degree measure of the whole circle)

$\mathsf{P(Blue)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{40}}{\color{#007DDC}{360}}$	Substitute values

	$=$	$\frac{1}{9}$

$(a) 1/2$

$(b) 1/9$

Question 6 of 7

Given the spinner below, find the probability of the arrow landing on:

$(a)$ Pink

$1$

$(b)$ an Even number

Write fractions in the format “a/b”

$(a)$ (1/5, 0.2)

$(b)$ (2/5, 0.4)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

Addition Principle

If two or more events are joined by OR, their probabilities should be added.

$(a)$ Find the probability of the arrow landing on Pink

$1$ .

favourable outcomes

$=$ $1$ (Pink

$1$ )

total outcomes

$=$ $5$ (Pink

$1$ , Green

$2$ , Orange

$3$ , Blue

$4$ , Yellow

$5$ )

$\mathsf{P(Pink\:}1\mathsf{)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{1}}{\color{#007DDC}{5}}$	Substitute values

$(b)$ Find the probability of the arrow landing on an Even number.

favourable outcomes

$=$ $2$ (Green

$2$ , Blue

$4$ )

total outcomes

$=$ $5$ (Pink

$1$ , Green

$2$ , Orange

$3$ , Blue

$4$ , Yellow

$5$ )

$\mathsf{P(Even)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{2}}{\color{#007DDC}{5}}$	Substitute values

$(a) 1/5$

$(b) 2/5$

Question 7 of 7

A six-sided dice has an uneven weight which causes the side with

$4$ dots to have twice the chance of any other side. Find the probability of rolling this dice and getting:

$(a) 4$

$(b)$ an Even number

Write fractions in the format “a/b”

$(a)$ (2/7, 0.29)

$(b)$ (4/7, 0.57)

Incorrect

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Probability Formula

$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$

Addition Principle

If two or more events are joined by OR, their probabilities should be added.

$(a)$ Find the probability of rolling the dice and getting

$4$ .

favourable outcomes

$=$ $2$ (

$4,4$ )

total outcomes

$=$ $7$ (

$1,2,3,4,4,5,6$ )

$\mathsf{P(}4\mathsf{)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{2}}{\color{#007DDC}{7}}$	Substitute values

$(b)$ Find the probability of rolling the dice and getting an Even number of dots.

favourable outcomes

$=$ $4$ (

$2,4,4,6$ )

total outcomes

$=$ $7$ (

$1,2,3,4,4,5,6$ )

$\mathsf{P(Even)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{4}}{\color{#007DDC}{7}}$	Substitute values

$(a) 2/7$

$(b) 4/7$

Simple Probability 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Range of Probability

2. Question

Hint

Excellent!

Probability Formula

3. Question

Hint

Keep Going!

Probability Formula

4. Question

Hint

Great Work!

Probability Formula

5. Question

Hint

Excellent!

Probability Formula

6. Question

Hint

Nice Job!

Probability Formula

Addition Principle

7. Question

Hint

Correct!

Probability Formula

Addition Principle

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