Mixing
How much of the total is percentage after a percentage?
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Imagine we have a pie and let $p,q$ be ratios between 0 and 1 (non-inclusive). If I first take $p$ out of the pie, and then $q$ out of the remainder, how much is that of the whole pie?
I can easily visualize that if $p=0.5$ so I take half of the pie, and then take again $q=0.5$ of the remainder, I will have taken a total of 0.75 of the pie. But how do I compute this in general for any $p$ and $q$?
percentages
asked Jul 26 at 19:36
advanced_learner
132
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up vote
2
down vote
favorite
Imagine we have a pie and let $p,q$ be ratios between 0 and 1 (non-inclusive). If I first take $p$ out of the pie, and then $q$ out of the remainder, how much is that of the whole pie?
I can easily visualize that if $p=0.5$ so I take half of the pie, and then take again $q=0.5$ of the remainder, I will have taken a total of 0.75 of the pie. But how do I compute this in general for any $p$ and $q$?
percentages
asked Jul 26 at 19:36
advanced_learner
132
After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Imagine we have a pie and let $p,q$ be ratios between 0 and 1 (non-inclusive). If I first take $p$ out of the pie, and then $q$ out of the remainder, how much is that of the whole pie?
I can easily visualize that if $p=0.5$ so I take half of the pie, and then take again $q=0.5$ of the remainder, I will have taken a total of 0.75 of the pie. But how do I compute this in general for any $p$ and $q$?
percentages
asked Jul 26 at 19:36
advanced_learner
132
Imagine we have a pie and let $p,q$ be ratios between 0 and 1 (non-inclusive). If I first take $p$ out of the pie, and then $q$ out of the remainder, how much is that of the whole pie?
I can easily visualize that if $p=0.5$ so I take half of the pie, and then take again $q=0.5$ of the remainder, I will have taken a total of 0.75 of the pie. But how do I compute this in general for any $p$ and $q$?
percentages
asked Jul 26 at 19:36
advanced_learner
132
asked Jul 26 at 19:36
advanced_learner
132
asked Jul 26 at 19:36
advanced_learner
132
asked Jul 26 at 19:36
advanced_learner
132
132
After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46
add a comment |Â
After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46
After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46
After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
The rule you want is
$$
pq
$$
when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is
$$
p + (1-p)q .
$$
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The rule you want is
$$
pq
$$
when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is
$$
p + (1-p)q .
$$
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
add a comment |Â
up vote
2
down vote
accepted
The rule you want is
$$
pq
$$
when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is
$$
p + (1-p)q .
$$
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The rule you want is
$$
pq
$$
when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is
$$
p + (1-p)q .
$$
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
The rule you want is
$$
pq
$$
when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is
$$
p + (1-p)q .
$$
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
edited Jul 26 at 19:54
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
answered Jul 26 at 19:43
Ethan Bolker
35.7k54199
35.7k54199
add a comment |Â
add a comment |Â
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After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total?
– NickD
Jul 26 at 19:46