Complementary Probability

Question 1 of 8

Find the probability of drawing a ball from this jar and getting:

$(i)$ a non-Brown ball

$(ii)$ a non-Orange ball

Write fractions in the format “a/b”

$(i)$ (3/8, ⅜)

$(ii)$ (5/8, ⅝)

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Probability Formula

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

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

$(i)$ Find the probability of not drawing a Brown ball

Start by finding the probability of drawing a Brown ball

favourable outcomes

$=$ $5$ (

$5$ Brown balls)

total outcomes

$=$ $8$ (

$8$ total balls)

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

	$=$	$\frac{\color{#e65021}{5}}{\color{#007DDC}{8}}$	Substitute values

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Brown})}$	$=$	$1-\mathsf{P(Brown)}$	Complementary Probability

	$=$	$1-\frac{5}{8}$	Substitute values

	$=$	$\frac{8}{8}-\frac{5}{8}$

	$=$	$\frac{3}{8}$

$(ii)$ Find the probability of not drawing an Orange ball

Start by finding the probability of drawing an Orange ball

favourable outcomes

$=$ $3$ (

$3$ Orange balls)

total outcomes

$=$ $8$ (

$8$ total balls)

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

	$=$	$\frac{\color{#e65021}{3}}{\color{#007DDC}{8}}$	Substitute values

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Orange})}$	$=$	$1-\mathsf{P(Orange)}$	Complementary Probability

	$=$	$1-\frac{3}{8}$	Substitute values

	$=$	$\frac{8}{8}-\frac{3}{8}$

	$=$	$\frac{5}{8}$

$(i) 3/8$

$(ii) 5/8$

Question 2 of 8

A six-sided dice has the letters

$C,H,A,N,C,E$ on its sides instead of numbers. Find the probability of rolling this dice and getting:

$(i)$ a non-

$C$ side

$(ii)$ a non-Vowel side

Write fractions in the format “a/b”

$(i)$ (2/3, ⅔)

$(ii)$ (2/3, ⅔)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

$(i)$ Find the probability rolling the dice and not getting

$C$

Start by finding the probability of getting

$C$

favourable outcomes

$=$ $2$ (

$C,C$ )

total outcomes

$=$ $6$ (

$C,H,A,N,C,E$ )

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

	$=$	$\frac{\color{#e65021}{2}}{\color{#007DDC}{6}}$	Substitute values

	$=$	$\frac{1}{3}$

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{C})}$	$=$	$1-\mathsf{P(C)}$	Complementary Probability

	$=$	$1-\frac{1}{3}$	Substitute values

	$=$	$\frac{3}{3}-\frac{1}{3}$

	$=$	$\frac{2}{3}$

$(ii)$ Find the probability rolling the dice and not getting a Vowel

Start by finding the probability of getting a Vowel

favourable outcomes

$=$ $2$ (

$A,E$ )

total outcomes

$=$ $6$ (

$C,H,A,N,C,E$ )

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

	$=$	$\frac{\color{#e65021}{2}}{\color{#007DDC}{6}}$	Substitute values

	$=$	$\frac{1}{3}$

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Vowel})}$	$=$	$1-\mathsf{P(Vowel)}$	Complementary Probability

	$=$	$1-\frac{1}{3}$	Substitute values

	$=$	$\frac{3}{3}-\frac{1}{3}$

	$=$	$\frac{2}{3}$

$(i) 2/3$

$(ii) 2/3$

Question 3 of 8

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

$(i)$ a non-Red card

$(ii)$ a non-King of Hearts card

Write fractions in the format “a/b”

$(i)$ (1/2, ½)

$(ii)$ (51/52)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

$(i)$ Find the probability drawing from a standard deck of cards and not getting a Red card

Start by finding the probability of drawing a Red card

favourable outcomes

$=$ $26$ (

$13$ Hearts cards,

$13$ Diamonds cards)

total outcomes

$=$ $52$ (a standard deck has

$52$ cards)

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

	$=$	$\frac{\color{#e65021}{26}}{\color{#007DDC}{52}}$	Substitute values

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

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Red})}$	$=$	$1-\mathsf{P(Red)}$	Complementary Probability

	$=$	$1-\frac{1}{2}$	Substitute values

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

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

$(ii)$ Find the probability drawing from a standard deck of cards and not getting a King of Hearts card

Start by finding the probability of drawing 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

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{King\:of\:Hearts})}$	$=$	$1-\mathsf{P(King\:of\:Hearts)}$	Complementary Probability

	$=$	$1-\frac{1}{52}$	Substitute values

	$=$	$\frac{52}{52}-\frac{1}{52}$

	$=$	$\frac{51}{52}$

$(i) 1/2$

$(ii) 51/52$

Question 4 of 8

Find the probability of drawing from a standard deck of cards and NOT getting an Even-numbered Club.

Write fractions in the format “a/b”

(47/52)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

Start by finding the probability of drawing an Even-numbered Club

favourable outcomes

$=$ $5$ (

$2,4,6,8,10$ of Clubs)

total outcomes

$=$ $52$ (a standard deck has

$52$ cards)

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

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

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Even\:Club})}$	$=$	$1-\mathsf{P(Even\:Club)}$	Complementary Probability

	$=$	$1-\frac{5}{52}$	Substitute values

	$=$	$\frac{52}{52}-\frac{5}{52}$

	$=$	$\frac{47}{52}$

$47/52$

Question 5 of 8

The wheel below will give dollar prizes depending on where the arrow points. Find the probability of NOT getting $5.

Write fractions in the format “a/b”

(7/8, ⅞)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

Start by finding the probability of getting $5

favourable outcomes

$=$ $1$ (

$5$ )

total outcomes

$=$ $8$ (

$5,10,20,50,100,100,100,100$ )

$\mathsf{P(5)}$	$=$	$\frac{\color{#e65021}{\mathsf{favourable\:outcomes}}}{\color{#007DDC}{\mathsf{total\:outcomes}}}$	Probability Formula

	$=$	$\frac{\color{#e65021}{1}}{\color{#007DDC}{8}}$	Substitute values

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{5})}$	$=$	$1-\mathsf{P(5)}$	Complementary Probability

	$=$	$1-\frac{1}{8}$	Substitute values

	$=$	$\frac{8}{8}-\frac{1}{8}$

	$=$	$\frac{7}{8}$

$7/8$

Question 6 of 8

A

$5$ pm bus has a record of being on time

$40$ out of its last

$50$ trips. Pete catches this

$5$ pm bus on weekdays everyday and uses it to travel home. What is the probability for this bus NOT to be on time?

Write fractions in the format “a/b”

(1/5)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

Start by finding the probability for this bus to be on time

favourable outcomes

$=$ $40$ (bus was on time on

$40$ trips)

total outcomes

$=$ $50$ (

$50$ total recorded trips)

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

	$=$	$\frac{\color{#e65021}{40}}{\color{#007DDC}{50}}$	Substitute values

	$=$	$\frac{4}{5}$

Substitute this into the Complementary Probability Formula

$\mathsf{P(not\:on\:time)}$	$=$	$1-\mathsf{P(on\:time)}$	Complementary Probability

	$=$	$1-\frac{4}{5}$	Substitute values

	$=$	$\frac{5}{5}-\frac{4}{5}$

	$=$	$\frac{1}{5}$

$1/5$

Question 7 of 8

A box contains

$8$ Red cards,

$3$ Green cards,

$12$ Black cards and

$7$ Blue cards. Find the probability of drawing a card from this box at random and getting:

$(i)$ a non-Black card

$(ii)$ a non-Blue card

Write fractions in the format “a/b”

$(i)$ (3/5)

$(ii)$ (23/30)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

$(i)$ Find the probability of not drawing a Black card

Start by finding the probability of drawing a Black card

favourable outcomes

$=$ $12$ (

$12$ Black)

total outcomes

$=$ $30$ (

$8$ Red,

$3$ Green,

$12$ Black,

$7$ Blue)

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

	$=$	$\frac{\color{#e65021}{12}}{\color{#007DDC}{30}}$	Substitute values

	$=$	$\frac{2}{5}$

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Black})}$	$=$	$1-\mathsf{P(Black)}$	Complementary Probability

	$=$	$1-\frac{2}{5}$	Substitute values

	$=$	$\frac{5}{5}-\frac{2}{5}$

	$=$	$\frac{3}{5}$

$(ii)$ Find the probability of not drawing a Blue card

Start by finding the probability of drawing a Blue card

favourable outcomes

$=$ $7$ (

$7$ Blue)

total outcomes

$=$ $30$ (

$8$ Red,

$3$ Green,

$12$ Black,

$7$ Blue)

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

	$=$	$\frac{\color{#e65021}{7}}{\color{#007DDC}{30}}$	Substitute values

Substitute this into the Complementary Probability formula

$\mathsf{P(\dot{Blue})}$	$=$	$1-\mathsf{P(Blue)}$	Complementary Probability

	$=$	$1-\frac{7}{30}$	Substitute values

	$=$	$\frac{30}{30}-\frac{7}{30}$

	$=$	$\frac{23}{30}$

$(i) 3/5$

$(ii) 23/30$

Question 8 of 8

A coin collection consists of

$\text(1/5)$ Australian coins,

$\text(13/100)$ US coins and

$\text(3/20)$ UK coins. Find the probability of choosing a coin from this collection at random and getting:

$(i)$ a non-Australian coin

$(ii)$ a non-US coin

$(iii)$ a non-UK coin

Write fractions in the format “a/b”

$(i)$ (4/5)

$(ii)$ (87/100)

$(iii)$ (17/20)

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Probability Formula

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

Complementary Probability

$\mathsf{P(\dot{E})}=1-\mathsf{P(E)}$

$(i)$ Find the probability of not choosing an Australian coin

$\mathsf{P(Aust)}=\frac{1}{5}$

$\mathsf{P(\dot{Aust})}$	$=$	$1-\mathsf{P(Aust)}$	Complementary Probability

	$=$	$1-\frac{1}{5}$	Substitute values

	$=$	$\frac{5}{5}-\frac{1}{5}$

	$=$	$\frac{4}{5}$

$(ii)$ Find the probability of not choosing a US coin

$\mathsf{P(US)}=\frac{13}{100}$

$\mathsf{P(\dot{US})}$	$=$	$1-\mathsf{P(US)}$	Complementary Probability

	$=$	$1-\frac{13}{100}$	Substitute values

	$=$	$\frac{100}{100}-\frac{13}{100}$

	$=$	$\frac{87}{100}$

$(iii)$ Find the probability of not choosing a UK coin

$\mathsf{P(UK)}=\frac{3}{20}$

$\mathsf{P(\dot{UK})}$	$=$	$1-\mathsf{P(UK)}$	Complementary Probability

	$=$	$1-\frac{3}{20}$	Substitute values

	$=$	$\frac{20}{20}-\frac{3}{20}$

	$=$	$\frac{17}{20}$

$(i) 4/5$

$(ii) 87/100$

$(iii) 17/20$

Complementary Probability

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