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Effectus [21]
3 years ago
10

Please help with 3 ASAP due TOMORROW

Mathematics
1 answer:
zheka24 [161]3 years ago
6 0
So, we know he submitted 3 already, and his teacher said that is 20%, let's say "x" is the 100%.

\bf \begin{array}{ccll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
3&20\\
x&100
\end{array}\implies \cfrac{3}{x}=\cfrac{20}{100}\implies \cfrac{3\cdot 100}{20}=x
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A closet contains n pairs of shoes. If 2r shoes are chosen at random, (where 2r < n), what is the probability that there will
Pie
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
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ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."

Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
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. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
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n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
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3 years ago
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Find the attachment below

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