Simple Probability 4
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Question 1 of 6
1. 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)` (1/3, 2/6, 0.33)`(b)` (1/6, 0.17)`(c)` (5/6, 0.83)
Hint
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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$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 2 of 6
2. 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)` (1/2, 3/6, 0.5)`(c)` (1/2, 3/6, 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.`(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 3 of 6
3. 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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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(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 4 of 6
4. Question
Find the probability of drawing from a standard deck of cards and getting:`(a)` Hearts`(b)` BlackWrite fractions in the format “a/b”-
`(a)` (1/4, 13/52, 0.25)`(b)` (1/2, 26/52, 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.`(a)` Find the probability of drawing from a standard deck of cards and getting a Hearts card.favourable outcomes`=``13` (a standard deck has `13` Hearts cards)total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(Hearts)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{13}}{\color{#007DDC}{52}}$$ Substitute values `=` $$\frac{1}{4}$$ `(b)` Find the probability of drawing from a standard deck of cards and getting a Black card.favourable outcomes`=``26` (a standard deck has `13` Spades and `13` Clubs cards)total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(Black)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{26}}{\color{#007DDC}{52}}$$ Substitute values `=` $$\frac{1}{2}$$ `(a) 1/4``(b) 1/2` -
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Question 5 of 6
5. Question
Find the probability of drawing from a standard deck of cards and getting:`(a)` Ace`(b) 6` of HeartsWrite fractions in the format “a/b”-
`(a)` (1/13, 4/52, 0.08)`(b)` (1/52, 0.02)
Hint
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$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$`(a)` Find the probability of drawing from a standard deck of cards and getting an Ace card.favourable outcomes`=4*1=``4` (each of the `4` suits has `1` Ace card)total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(Ace)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{4}}{\color{#007DDC}{52}}$$ Substitute values `=` $$\frac{1}{13}$$ `(b)` Find the probability of drawing from a standard deck of cards and getting a `6` of Hearts card.favourable outcomes`=``1` (there is only one `6` of Hearts )total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(}6\:\mathsf{of\:Hearts)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{52}}$$ Substitute values `(a) 4/52` or `1/13``(b) 1/52` -
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Question 6 of 6
6. Question
Find the probability of drawing from a standard deck of cards and getting:`(a)` King of Hearts`(b) 6`Write fractions in the format “a/b”-
`(a)` (1/52, 0.02)`(b)` (4/52, 1/13, 0.08)
Hint
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Great Work!
Incorrect
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 drawing from a standard deck of cards and getting a King of Hearts card.favourable outcomes`=``1` (there is only `1` King of Hearts card)total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(King\:of\:Hearts)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{1}}{\color{#007DDC}{52}}$$ Substitute values `(b)` Find the probability of drawing from a standard deck of cards and getting a `6` card.favourable outcomes`=4*1=``4` (each of the `4` suits have one `6` card )total outcomes`=``52` (a standard deck has `52` cards)$$ \mathsf{P(}6\mathsf{)} $$ `=` $$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$ Probability Formula `=` $$\frac{\color{#e65021}{4}}{\color{#007DDC}{52}}$$ Substitute values `=` $$\frac{1}{13}$$ `(a) 1/52``(b) 4/52` or `1/13` -
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)