Simple Probability 2
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Question 1 of 7
1. Question
Find the probability of tossing a normal coin and getting:`(i)` Heads`(ii)` TailsWrite fractions in the format “a/b”-
`(i)` (1/2, 50/100, 0.5, 5/10)`(ii)` (1/2, 50/100, 0.5, 5/10)
Hint
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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(i)` Find the probability of getting Heads from the coin toss.favourable outcomes`=``1` (Heads)total outcomes`=``2` (Heads, Tails)$$ \mathsf{P(H)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{2}}$$ Substitute values `(ii)` Find the probability of getting Tails from the coin toss.favourable outcomes`=``1` (Tails)total outcomes`=``2` (Heads, Tails)$$ \mathsf{P(T)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{2}}$$ Substitute values `(i) 1/2``(ii) 1/2` -
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Question 2 of 7
2. Question
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:`(a)` Jake will win`(b)` Emma will winWrite fractions in the format “a/b”-
`(a)` (1/10, 10/100, 0.1)`(b)` (1/20, 10/200, 0.05)
Hint
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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(a)` Find the probability that Jake will win.favourable outcomes`=``10` (Jake bought `10` tickets)total outcomes`=``100` (the barrel holds `100` tickets)$$ \mathsf{P(Jake)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{10}}{\color{#007DDC}{100}}$$ Substitute values `=` $$\frac{1}{10}$$ `(b)` Find the probability that Emma will win.favourable outcomes`=``5` (Emma bought `5` tickets)total outcomes`=``100` (the barrel holds `100` tickets)$$ \mathsf{P(Emma)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{5}}{\color{#007DDC}{100}}$$ Substitute values `=` $$\frac{1}{20}$$ `(a) 1/10``(b) 1/20` -
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Question 3 of 7
3. Question
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:
`(a)` How many tickets should she buy to have a certain chance at winning?`(b)` How many tickets should she buy to have a `50%` chance at winning?Write fractions in the format “a/b”-
`(a)` (16) tickets`(b)` (8, 16/2) tickets
Hint
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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(a)` Find the number of tickets she should buy to have a certain chance at winning.favourable outcomes`=``x` (number of tickets she should buy)total outcomes`=``16` (the wheel has `16` sectors)P(certain)`=100%=1`$$ \mathsf{P(certain)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula $$1$$ `=` $$\frac{\color{#e65021}{x}}{\color{#007DDC}{16}}$$ Substitute values `1``times16` `=` `x/16``times16` Multiple both sides by `16` `16` `=` `x` `x` `=` `16` `(b)` Find the number of tickets she should buy to have a `50%` chance at winning.favourable outcomes`=``x` (number of tickets she should buy)total outcomes`=``16` (the wheel has `16` sectors)P(50%)`=1/2`$$ \mathsf{P(}50\%\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `1/2` `=` $$\frac{\color{#e65021}{x}}{\color{#007DDC}{16}}$$ Substitute values `1/2``times16` `=` `x/16``times16` Multiple both sides by `16` `8` `=` `x` `x` `=` `8` `(a) 16` tickets`(b) 8` tickets -
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Question 4 of 7
4. 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)` (1/3, 2/6, 0.33)
Hint
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Help VideoProbability 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 5 of 7
5. 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)` (1/3, 120/360, 0.33)
Hint
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Help VideoProbability 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 6 of 7
6. 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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Help VideoProbability 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 7 of 7
7. 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)` (1/2, 3/6, 0.5)`(b)` (2/3, 4/6, 0.67)`(c)` (0/6, 0)
Hint
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Well Done!
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Help VideoProbability 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` -
Quizzes
- Simple Probability 1
- Simple Probability 2
- Simple Probability 3
- Simple Probability 4
- Complementary Probability 1
- Compound Events 1
- Compound Events 2
- Venn Diagrams (Non Mutually Exclusive)
- Independent Events 1
- Independent Events 2
- Dependent Events (Conditional Probability)
- Probability Tree (Independent)
- Probability Tree (Dependent)