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Simple Probability (Theoretical) 1Simple Probability (Theoretical) 1
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Question 1 of 7
1. Question
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)` ImpossibleWrite fractions in the format “a/b”-
`(i)` Certain `=` (1, 1/1, 100/100)`(ii)` Even Chance `=` (½, 1/2, 0.5, 50/100)`(iii)` Impossible `=` (0, 0/1, 0/100)
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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 probabilitycertain`=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 probabilityimpossible`=0``(i) 1``(ii) 1/2` or `0.5``(iii) 0` -
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Question 2 of 7
2. Question
Find the probability of tossing a normal coin and getting:`(i)` Heads`(ii)` TailsWrite fractions in the format “a/b”-
`(i)` (½, 1/2, 50/100, 0.5, 5/10)`(ii)` (½, 1/2, 50/100, 0.5, 5/10)
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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 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 3 of 7
3. Question
Find the probability of spinning the following spinners and getting:
`(i)` Orange
`(ii)` PinkWrite fractions in the format “a/b”-
`(i)` (½, 1/2, 2/4, 0.5)`(ii)` (1/5, 0.2)
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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` -
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Question 4 of 7
4. 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, 5/100, 10/200, 0.05)
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Probability Formula
$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(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 5 of 7
5. 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:`(c)` Dylan will win`(d)` None of them will winWrite fractions in the format “a/b”-
`(c)` (1/100, 0.01)`(d)` (84/100, 21/25, 0.84)
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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` -
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Question 6 of 7
6. 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
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Probability Formula
$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(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 7 of 7
7. 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:`(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)` (⅜, 3/8, 6/16, 0.375, 0.38)
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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` -
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)