Simple Probability 4

Question 1 of 6

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)

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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

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)

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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.

$(c)$ 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

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)

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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 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

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)

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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.

$(c)$ 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

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)

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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 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

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)

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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.

$(c)$ 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

$1/26$

$(d) 5/52$

Simple Probability 4

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Quiz summary

Information

1. Question

Hint

Well Done!

Probability Formula

Addition Principle

2. Question

Hint

Correct!

Probability Formula

Addition Principle

3. Question

Hint

Great Work!

Probability Formula

4. Question

Hint

Well Done!

Probability Formula

Addition Principle

5. Question

Hint

Great Work!

Probability Formula

Addition Principle

6. Question

Hint

Exceptional!

Probability Formula

Addition Principle

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