Simple Probability (Theoretical) 4

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Year 12

Probability

Simple Probability (Theoretical)

Simple Probability (Theoretical) 4

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Question 1 of 6

1. Question

Find the probability of drawing from a standard deck of cards and getting:

`(a)` Hearts

`(b)` Black

Write fractions in the format “a/b”

`(a)` (¼, 1/4, 13/52, 0.25)

`(b)` (½, 1/2, 26/52, 0.5)

Hint

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Correct

Well Done!

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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 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`

Question 2 of 6

2. Question

Find the probability of drawing from a standard deck of cards and getting:

`(c)` Picture

`(d)` Red or Black

Write fractions in the format “a/b”

`(c)` (3/13, 12/52, 0.23)

`(d)` (1, 52/52)

Hint

Help Video

Correct

Correct!

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 drawing from a standard deck of cards and getting a Picture card.

favourable outcomes`=3*4=``12` (a standard deck has `3` Picture cards for each of the `4` suits)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Picture)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{12}}{\color{#007DDC}{52}}$$	Substitute values

	`=`	$$\frac{3}{13}$$

`(d)` Find the probability of drawing from a standard deck of cards and getting a Red or Black card.

favourable outcomes`=``52` (all cards from a standard deck are either Red or Black)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Red\:or\:Black)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{52}}{\color{#007DDC}{52}}$$	Substitute values

	`=`	$$1$$

`(c) 3/13`

`(d) 1`

Question 3 of 6

3. Question

Find the probability of drawing from a standard deck of cards and getting:

`(a)` Ace

`(b) 6` of Hearts

Write fractions in the format “a/b”

`(a)` (1/13, 4/52, 0.08)

`(b)` (1/52, 0.02)

Hint

Help Video

Correct

Great Work!

Incorrect

Probability Formula

$$\mathsf{P(E)}=\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$

`(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`

Question 4 of 6

4. Question

Find the probability of drawing from a standard deck of cards and getting:

`(c)` Red or a Black `9`

`(d)` Red `4`

Write fractions in the format “a/b”

`(c)` (7/13, 28/52, 0.52)

`(d)` (2/52, 1/26, 0.04)

Hint

Help Video

Correct

Well Done!

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 drawing from a standard deck of cards and getting a Red or a Black `9` card.

favourable outcomes`=26+1+1=``28` (`26` Red, one `9` of Clubs, one `9` of Spades)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Red\:or\:a\:Black\:}9\mathsf{)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{28}}{\color{#007DDC}{52}}$$	Substitute values

	`=`	$$\frac{7}{13}$$

`(d)` Find the probability of drawing from a standard deck of cards and getting a Red `4` card.

favourable outcomes`=``2` (one `4` of Hearts, one `4` of Diamonds)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Red\:}4\mathsf{)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{2}}{\color{#007DDC}{52}}$$	Substitute values

	`=`	$$\frac{1}{26}$$

`(c) 28/52` or `7/13`

`(d) 2/52` or `1/26`

Question 5 of 6

5. 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

Help Video

Correct

Great Work!

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.

`(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`

Question 6 of 6

6. Question

Find the probability of drawing from a standard deck of cards and getting:

`(c)` Black Jack

`(d)` Queen or `3` of Diamonds

Write fractions in the format “a/b”

`(c)` (2/52, 1/26, 0.04)

`(d)` (5/52, [0.10)

Hint

Help Video

Correct

Exceptional!

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 drawing from a standard deck of cards and getting a Black Jack.

favourable outcomes`=``2` (`1` Jack of Spades, `1` Jack of Clubs)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Black\:Jack)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{2}}{\color{#007DDC}{52}}$$	Substitute values

	`=`	$$\frac{1}{26}$$

`(d)` Find the probability of drawing from a standard deck of cards and getting a Queen or a `3` of Diamonds card.

favourable outcomes`=(4*1)+1=``5` (each of the `4` suits have `1` Queen card, one `3` of Diamonds)

total outcomes`=``52` (a standard deck has `52` cards)

$$ \mathsf{P(Queen\:or\:}3\:\mathsf{of\:Diamonds)} $$	`=`	$$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$$	Probability Formula

	`=`	$$\frac{\color{#e65021}{5}}{\color{#007DDC}{52}}$$	Substitute values

`(c) 2/52` or `1/26`

`(d) 5/52`

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