Simple Probability 4

Question 1 of 6

A six-sided dice does not have a side with

6

$6$ dots but instead has two sides with

1

$1$ dot. Find the probability of the rolling the dice and getting:

(a) 1

$(a) 1$

(b) 3

$(b) 3$

(c) 4

$(c) 4$ or less

Write fractions in the format “a/b”

$(a)$ $(a)$ (1/3, 2/6, 0.33)

$(b)$ $(b)$ (1/6, 0.17)

$(c)$ $(c)$ (5/6, 0.83)

Incorrect

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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

$2/6$

$(b) 1/6$

$(c) 5/6$

Question 2 of 6

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 dots

Write 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)

Incorrect

Help Video

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

	$=$	$\frac{1}{2}$

$(a) 1/6$

$(b) 1/2$

$(c) 1/2$

Question 3 of 6

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

$(b)$ Yellow

Write fractions in the format “a/b”

$(a)$ (5/14, 0.36)

$(b)$ (3/7, 6/14, 0.43)

Incorrect

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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

	$=$	$\frac{3}{7}$

$(a) 5/14$

$(b) 3/7$

Question 4 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”

$(a)$ (1/4, 13/52, 0.25)

$(b)$ (1/2, 26/52, 0.5)

Incorrect

Help Video

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 5 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)

Incorrect

Help Video

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 6 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)

Incorrect

Help Video

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

$1/13$

Simple Probability 4

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1. Question

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Addition Principle

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