Simple Probability (Theoretical) 4

Question 1 of 6

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

(a)

$(a)$ Hearts

(b)

$(b)$ Black

Write fractions in the format “a/b”

$(a)$ $(a)$ (¼, 1/4, 13/52, 0.25)

$(b)$ $(b)$ (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 (Theoretical) 4

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Quiz summary

Information

1. Question

Hint

Well Done!

Probability Formula

Addition Principle

2. Question

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Correct!

Probability Formula

Addition Principle

3. Question

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Great Work!

Probability Formula

4. Question

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Well Done!

Probability Formula

Addition Principle

5. Question

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Great Work!

Probability Formula

Addition Principle

6. Question

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Exceptional!

Probability Formula

Addition Principle

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