Complementary Probability 1
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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 ballWrite fractions in the format “a/b”-
`(i)` (3/8, ⅜)`(ii)` (5/8, ⅝)
Hint
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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 Brown ballStart by finding the probability of drawing a Brown ballfavourable 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 ballStart by finding the probability of drawing an Orange ballfavourable 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` -
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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 sideWrite fractions in the format “a/b”-
`(i)` (2/3, ⅔)`(ii)` (2/3, ⅔)
Hint
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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 VowelStart by finding the probability of getting a Vowelfavourable 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` -
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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 cardWrite fractions in the format “a/b”-
`(i)` (1/2, ½)`(ii)` (51/52)
Hint
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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 cardStart by finding the probability of drawing a Red cardfavourable 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 cardStart by finding the probability of drawing a King of Hearts cardfavourable 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` -
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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
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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 Clubfavourable 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
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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 $5favourable 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
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Correct!
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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 timefavourable 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 cardWrite fractions in the format “a/b”-
`(i)` (3/5)`(ii)` (23/30)
Hint
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Great Work!
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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 cardStart by finding the probability of drawing a Black cardfavourable 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 cardStart by finding the probability of drawing a Blue cardfavourable 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` -
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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 coinWrite fractions in the format “a/b”-
`(i)` (4/5)`(ii)` (87/100)`(iii)` (17/20)
Hint
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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` -