Complementary Probability

Years

Try VividMath Premium to unlock full access

Start Free Trial

Time limit: 0

Quiz summary

0 of 8 questions completed

Questions:

Information

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 8

1. Question

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)

Hint

Help Video

Correct

Well Done!

Incorrect

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

2. Question

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)

Hint

Help Video

Correct

Nice Job!

Incorrect

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

3. Question

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)

Hint

Help Video

Correct

Excellent!

Incorrect

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

4. Question

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)

Hint

Help Video

Correct

Fantastic!

Incorrect

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

5. Question

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)

Hint

Help Video

Correct

Keep Going!

Incorrect

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

6. Question

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)

Hint

Help Video

Correct

Correct!

Incorrect

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

7. Question

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)

Hint

Help Video

Correct

Great Work!

Incorrect

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

8. Question

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)

Hint

Help Video

Correct

Excellent!

Incorrect

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`

Quizzes

Simple Probability (Theoretical) 1
Simple Probability (Theoretical) 2
Simple Probability (Theoretical) 3
Simple Probability (Theoretical) 4
Complementary Probability
Compound Events (Addition Rule) 1
Compound Events (Addition Rule) 2
Venn Diagrams (Mutually Inclusive)
Independent Events 1
Independent Events 2
Dependent Events (Conditional Probability)
Probability Tree (Independent Events) 1
Probability Tree (Independent Events) 2
Probability Tree (Dependent Events)