Simple Probability 2

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Question 1 of 7

1. Question

Find the probability of rolling a six-sided dice and getting:

`(i) 2`

`(ii) 4` or `5`

Write fractions in the format “a/b”

`(i)` (1/6, 0.17)

`(ii)` (⅓, 1/3, 2/6, 0.33)

Hint

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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.

`(i)` Find the probability of rolling a six-sided dice and getting `2`.

favourable outcomes`=``1` (`2`)

total outcomes`=``6` (`1,2,3,4,5,6`)

$$ \mathsf{P(}2\mathsf{)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{1}}{\color{#007DDC}{6}}$$	Substitute values

`(ii)` Find the probability of rolling a six-sided dice and getting `4` or `5`.

favourable outcomes`=``2` (`4,5`)

total outcomes`=``6` (`1,2,3,4,5,6`)

$$ \mathsf{P(}4\:\mathsf{or}\:5\mathsf{)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{2}}{\color{#007DDC}{6}}$$	Substitute values

	`=`	$$\frac{1}{3}$$

`(i) 1/6`

`(ii) 1/3`

Question 2 of 7

2. Question

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)` (½, 1/2, 180/360, 0.5)

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

Hint

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Correct

Excellent!

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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 3 of 7

3. Question

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

`(c)` not Red

`(d)` Blue or Orange

Write fractions in the format “a/b”

`(c)` (5/6, 300/360, 0.83)

`(d)` (⅓, 1/3, 120/360, 0.33)

Hint

Help Video

Correct

Well Done!

Incorrect

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.

`(c)` Find the probability of the arrow NOT landing on Red.

favourable outcomes`=360-60=``300` (degree measure of the sector without Red)

total outcomes`=``360` (degree measure of the whole circle)

$$ \mathsf{P(not\:Red)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{300}}{\color{#007DDC}{360}}$$	Substitute values

	`=`	$$\frac{5}{6}$$

`(d)` Find the probability of the arrow landing on Blue or Orange.

favourable outcomes`=40+80=``120` (degree measure of Blue`+`Orange)

total outcomes`=``360` (degree measure of the whole circle)

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

	`=`	$$\frac{\color{#e65021}{120}}{\color{#007DDC}{360}}$$	Substitute values

	`=`	$$\frac{1}{3}$$

`(c) 5/6`

`(d) 1/3`

Question 4 of 7

4. Question

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)

Hint

Help Video

Correct

Nice Job!

Incorrect

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 5 of 7

5. Question

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

`(c)` an Odd number

`(d)` Zero

Write fractions in the format “a/b”

`(c)` (3/5, 0.6)

`(d)` (0, 0/5)

Hint

Help Video

Correct

Fantastic!

Incorrect

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.

`(c)` Find the probability of the arrow landing on an Odd number.

favourable outcomes`=``3` (Pink `1`, Orange `3`, Yellow `5`)

total outcomes`=``5` (Pink `1`, Green `2`, Orange `3`, Blue `4`, Yellow `5`)

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

	`=`	$$\frac{\color{#e65021}{3}}{\color{#007DDC}{5}}$$	Substitute values

`(d)` Find the probability of the arrow landing on Zero.

favourable outcomes`=``0` (the Spinner has no sector with `0`)

total outcomes`=``5` (Pink `1`, Green `2`, Orange `3`, Blue `4`, Yellow `5`)

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

	`=`	$$\frac{\color{#e65021}{0}}{\color{#007DDC}{5}}$$	Substitute values

	`=`	$$0$$

`(c) 3/5`

`(d) 0`

Question 6 of 7

6. Question

A six-sided dice has `1` dot placed on the sides where there should be `2` and `3` while all the other sides have not been changed. Find the probability of rolling the dice and getting:

`(a) 1`

`(b)` an Odd number

`(c) 2`

Write fractions in the format “a/b”

`(a)` (½, 1/2, 3/6, 0.5)

`(b)` (⅔, 2/3, 4/6, 0.67)

`(c)` (0/6, 0)

Hint

Help Video

Correct

Well Done!

Incorrect

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 `1`.

favourable outcomes`=``3` (`1,1,1`)

total outcomes`=``6` (`1,1,1,4,5,6`)

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

	`=`	$$\frac{\color{#e65021}{3}}{\color{#007DDC}{6}}$$	Substitute values

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

`(b)` Find the probability of rolling the dice and getting an Odd number of dots.

favourable outcomes`=``4` (`1,1,1,5`)

total outcomes`=``6` (`1,1,1,4,5,6`)

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

	`=`	$$\frac{\color{#e65021}{4}}{\color{#007DDC}{6}}$$	Substitute values

	`=`	$$\frac{2}{3}$$

`(c)` Find the probability of rolling the dice and getting `2`.

favourable outcomes`=``0` (no side has `2` dots)

total outcomes`=``6` (`1,1,1,4,5,6`)

$$ \mathsf{P(}2\mathsf{)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{0}}{\color{#007DDC}{6}}$$	Substitute values

	`=`	$$0$$

`(a) 1/2`

`(b) 2/3`

`(c) 0`

Question 7 of 7

7. Question

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)

Hint

Help Video

Correct

Correct!

Incorrect

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`

Quizzes

Simple Probability 1
Simple Probability 2
Simple Probability 3
Simple Probability 4
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Compound Events 1
Compound Events 2
Venn Diagrams (Non Mutually Exclusive)
Independent Events 1
Independent Events 2
Dependent Events (Conditional Probability)
Probability Tree (Independent) 1
Probability Tree (Independent) 2
Probability Tree (Dependent)