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Simple Probability (Theoretical) 3Simple Probability (Theoretical) 3
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Question 1 of 7
1. Question
Find the probability of spinning the following spinners and getting:
`(i)` Pink or Green
`(ii)` Yellow or BlueWrite fractions in the format “a/b”-
`(i)` (2/5, 0.4)`(ii)` (¾, 3/4, 0.75)
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 the arrow landing on Pink or Green.
favourable outcomes`=``2` (`1` Pink `+1` Green)total outcomes`=``5` (Pink, Green, Orange, Blue, Yellow)$$ \mathsf{P(Pink\:or\:Green)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{2}}{\color{#007DDC}{5}}$$ Substitute values `(ii)` Find the probability of the arrow landing on Yellow or Blue.
favourable outcomes`=``3` (`2` Yellow `+1` Blue)total outcomes`=``4` (Orange, Blue, and `2` Yellow)$$ \mathsf{P(Yellow\:or\:Blue)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{3}}{\color{#007DDC}{4}}$$ Substitute values `(i) 2/5``(ii) 3/4` -
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Question 2 of 7
2. Question
A six-sided dice does not have a side with `6` dots but instead has two sides with `1` dot. Find the probability of the rolling the dice and getting:`(a) 1``(b) 3``(c) 4` or lessWrite fractions in the format “a/b”-
`(a)` (⅓, 1/3, 2/6, 0.33)`(b)` (1/6, 0.17)`(c)` (5/6, 0.83)
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`=``2` (`1,1`)total outcomes`=``6` (`1,1,2,3,4,5`)$$ \mathsf{P(}1\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{2}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{1}{3}$$ `(b)` Find the probability of rolling the dice and getting `3`.favourable outcomes`=``1` (`3`)total outcomes`=``6` (`1,1,2,3,4,5`)$$ \mathsf{P(}3\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{6}}$$ Substitute values `(c)` Find the probability of rolling the dice and getting `4` or less.favourable outcomes`=``5` (`1,1,2,3,4`)total outcomes`=``6` (`1,1,2,3,4,5`)$$ \mathsf{P(}4\:\mathsf{or\:less)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{5}}{\color{#007DDC}{6}}$$ Substitute values `(a) 1/3` or `2/6``(b) 1/6``(c) 5/6` -
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Question 3 of 7
3. Question
A six-sided dice does not have a side with `6` dots but instead has two sides with `1` dot. Find the probability of the rolling the dice and getting:`(d) 6``(e)` greater than `1`Write fractions in the format “a/b”-
`(d)` (0, 0/6)`(e)` (⅔, 2/3, 4/6, 0.67)
Hint
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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.`(d)` Find the probability of rolling the dice and getting `6`.favourable outcomes`=``0` (no sides have `6` dots)total outcomes`=``6` (`1,1,2,3,4,5`)$$ \mathsf{P(}6\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{0}}{\color{#007DDC}{6}}$$ Substitute values `=` $$0$$ `(e)` Find the probability of rolling the dice and getting greater than `1`.favourable outcomes`=``4` (`2,3,4,5`)total outcomes`=``6` (`1,1,2,3,4,5`)$$ \mathsf{P(greater\:than\:}1\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{4}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{2}{3}$$ `(d) 0``(e) 4/6` or `2/3` -
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Question 4 of 7
4. Question
A normal six-sided dice is rolled. Find the probability of getting:`(a) 5``(b)` an Odd number of dots`(c)` an Even number of dotsWrite fractions in the format “a/b”-
`(a)` (1/6, 0.17)`(b)` (½, 1/2, 3/6, 0.5)`(c)` (½, 1/2, 3/6, 0.5)
Hint
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Keep Going!
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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 rolling the dice and getting `5`.favourable outcomes`=``1` (`5`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(}5\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{6}}$$ Substitute values `(b)` Find the probability of the rolling the dice and getting an Odd number of dots.favourable outcomes`=``3` (`1,3,5`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(Odd)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{3}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{1}{2}$$ `(c)` Find the probability of the rolling the dice and getting an Even number of dots.favourable outcomes`=``3` (`2,4,6`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(Even)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{3}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{1}{2}$$ `(a) 1/6``(b) 1/2``(c) 1/2` -
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Question 5 of 7
5. Question
A normal six-sided dice is rolled. Find the probability of getting:`(d) 3` or `6``(e) gt 3``(f) lt 7`Write fractions in the format “a/b”-
`(d)` (⅓, 1/3, 2/6, 0.17)`(e)` (½, 1/2, 3/6, 0.5)`(f)` (1, 6/6)
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.`(d)` Find the probability of the rolling the dice and getting `3` or `6`.favourable outcomes`=``2` (`3,6`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(}3\:\mathsf{or}\:6\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{2}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{1}{3}$$ `(e)` Find the probability of the rolling the dice and getting `>“3`.favourable outcomes`=``3` (`4,5,6`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(}>3\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{3}}{\color{#007DDC}{6}}$$ Substitute values `=` $$\frac{1}{2}$$ `(f)` Find the probability of the rolling the dice and getting `<“7`.favourable outcomes`=``6` (`1,2,3,4,5,6`)total outcomes`=``6` (`1,2,3,4,5,6`)$$ \mathsf{P(}<7\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{6}}{\color{#007DDC}{6}}$$ Substitute values `=` $$1$$ `(d) 1/3``(e) 1/2``(f) 1` -
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Question 6 of 7
6. Question
A jar contains `5` red marbles, `6` yellow marbles and `3` black marbles. Find the probability of drawing a marble at random and getting:`(a)` Red`(b)` YellowWrite fractions in the format “a/b”-
`(a)` (5/14, 0.36)`(b)` (3/7, 6/14, 0.43)
Hint
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Great Work!
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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 drawing a marble at random and getting a Red marble.favourable outcomes`=``5` (`5` Red)total outcomes`=``14` (`5` Red, `6` Yellow, `3` Black)$$ \mathsf{P(Red)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{5}}{\color{#007DDC}{14}}$$ Substitute values `(b)` Find the probability of the drawing a marble at random and getting a Yellow marble.favourable outcomes`=``6` (`6` Red)total outcomes`=``14` (`5` Red, `6` Yellow, `3` Black)$$ \mathsf{P(Yellow)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{6}}{\color{#007DDC}{14}}$$ Substitute values `=` $$\frac{3}{7}$$ `(a) 5/14``(b) 3/7` -
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Question 7 of 7
7. Question
A jar contains `5` red marbles, `6` yellow marbles and `3` black marbles. Find the probability of drawing a marble at random and getting:`(c)` Black or Red`(d)` BlueWrite fractions in the format “a/b”-
`(c)` (4/7, 8/14, 0.57)`(d)` (0, 0/14)
Hint
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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 drawing a marble at random and getting a Black or Red marble.favourable outcomes`=``8` (`3` Black, `5` Red)total outcomes`=``14` (`5` Red, `6` Yellow, `3` Black)$$ \mathsf{P(Black\:or\:Red)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{8}}{\color{#007DDC}{14}}$$ Substitute values `=` $$\frac{4}{7}$$ `(d)` Find the probability of the drawing a marble at random and getting a Blue marble.favourable outcomes`=``0` (there are no Blue marbles)total outcomes`=``14` (`5` Red, `6` Yellow, `3` Black)$$ \mathsf{P(Blue)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{0}}{\color{#007DDC}{14}}$$ Substitute values `=` $$0$$ `(c) 4/7``(d) 0` -
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)