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Simple Probability (Theoretical) 2Simple Probability (Theoretical) 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` -
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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)` BlueWrite 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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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` -
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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 OrangeWrite fractions in the format “a/b”-
`(c)` (5/6, 300/360, 0.83)`(d)` (⅓, 1/3, 120/360, 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.`(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` -
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Question 4 of 7
4. Question
Given the spinner below, find the probability of the arrow landing on:
`(a)` Pink `1``(b)` an Even numberWrite fractions in the format “a/b”-
`(a)` (1/5, 0.2)`(b)` (2/5, 0.4)
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.`(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` -
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Question 5 of 7
5. Question
Given the spinner below, find the probability of the arrow landing on:
`(c)` an Odd number`(d)` ZeroWrite fractions in the format “a/b”-
`(c)` (3/5, 0.6)`(d)` (0, 0/5)
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.`(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` -
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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
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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` -
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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 numberWrite fractions in the format “a/b”-
`(a)` (2/7, 0.29)`(b)` (4/7, 0.57)
Hint
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Correct!
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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` -
Quizzes
- Simple Probability (Theoretical) 1
- Simple Probability (Theoretical) 2
- Simple Probability (Theoretical) 3
- Simple Probability (Theoretical) 4
- Complementary Probability
- Compound Events (Addition Rule) 1
- Compound Events (Addition Rule) 2
- Venn Diagrams (Mutually Inclusive)
- Independent Events 1
- Independent Events 2
- Dependent Events (Conditional Probability)
- Probability Tree (Independent Events) 1
- Probability Tree (Independent Events) 2
- Probability Tree (Dependent Events)