Simple Probability (Theoretical) 2

Question 1 of 7

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

(i) 2

$(i) 2$

(i i) 4

$(ii) 4$ or

5

$5$

Write fractions in the format “a/b”

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

$(i i)$ $(ii)$ (⅓, 1/3, 2/6, 0.33)

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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

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)

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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

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)

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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.

$(c)$ 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

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)

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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 5 of 7

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)

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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.

$(c)$ 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

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)

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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

$1$ .

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

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)

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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 (Theoretical) 2

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