Simple Probability 4
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Question 1 of 6
1. Question
Find the probability of drawing from a standard deck of cards and getting:`(a)` Hearts`(b)` BlackWrite fractions in the format “a/b”-
`(a)` (¼, 1/4, 13/52, 0.25)`(b)` (½, 1/2, 26/52, 0.5)
Hint
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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` -
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Question 2 of 6
2. Question
Find the probability of drawing from a standard deck of cards and getting:`(c)` Picture`(d)` Red or BlackWrite fractions in the format “a/b”-
`(c)` (3/13, 12/52, 0.23)`(d)` (1, 52/52)
Hint
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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` -
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Question 3 of 6
3. Question
Find the probability of drawing from a standard deck of cards and getting:`(a)` Ace`(b) 6` of HeartsWrite fractions in the format “a/b”-
`(a)` (1/13, 4/52, 0.08)`(b)` (1/52, 0.02)
Hint
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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` -
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Question 4 of 6
4. Question
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)
Hint
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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` -
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Question 5 of 6
5. Question
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)
Hint
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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` -
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Question 6 of 6
6. Question
Find the probability of drawing from a standard deck of cards and getting:`(c)` Black Jack`(d)` Queen or `3` of DiamondsWrite fractions in the format “a/b”-
`(c)` (2/52, 1/26, 0.04)`(d)` (5/52, [0.10)
Hint
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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` -