Probability questions explanation needed

[malcolmmalcolmm]

1)There are 2 yellow balls in a box. How many red balls need to be added if
we want exactly 21 different orders of drawing all the balls?

2)
Suppose a kangoroo lives on the real line and can perform unit length jumps
in either the positive or negative direction. How many different ways can
he find to get from 0 to 3 in 15 jumps? Ex: +-+-+-++-+-+-++


3)
There is a pandemic in Absurdistan. At any time there is a 70% chance
that someone has the disease. Luckily there is a test for infection, but of
the tests performed, 10% gave a false positive result and 5% of them gave
a false negative. If you got a positive result from the test, what is the
probability that you are really infected? If you tested negative, what is the
probability that you are not infected?

 

[Deleted member 4993]

1)There are 2 yellow balls in a box. How many red balls need to be added if
we want exactly 21 different orders of drawing all the balls?

2) Suppose a kangoroo lives on the real line and can perform unit length jumps
in either the positive or negative direction. How many different ways can
he find to get from 0 to 3 in 15 jumps? Ex: +-+-+-++-+-+-++

3) There is a pandemic in Absurdistan. At any time there is a 70% chance
that someone has the disease. Luckily there is a test for infection, but of
the tests performed, 10% gave a false positive result and 5% of them gave
a false negative. If you got a positive result from the test, what is the
probability that you are really infected? If you tested negative, what is the
probability that you are not infected?

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[HallsofIvy]

You seem to be misunderstanding the purpose of this site. We help you with math problems, not do them for you! And to do that it helps to know what you already understand about a problem and what you can already do.

Here's how I would think about the third problem:

There is a pandemic in Absurdistan. At any time there is a 70% chance
that someone has the disease. Luckily there is a test for infection, but of
the tests performed, 10% gave a false positive result and 5% of them gave
a false negative. If you got a positive result from the test, what is the
probability that you are really infected? If you tested negative, what is the
probability that you are not infected?

Imagine a population of 1000. 70%, 700, have the disease, 300 do not. Of the 700 who have the disease, 5%, 35, test negative, the other 665 test positive. Of the 300 who do not have the disease, 10%, 30, test positive, the other 270 test negative.

So a total of 665+ 30= 695 test positive of whom 665 actually have the disease.

Can you finish?

 

[pka]

Can you solve \(\dfrac{(y+2)!}{2!\cdot y!}=21~?\)

 

[HallsofIvy]

It is useful to know that (y+ 2)!= (y+ 1)(y+ 1)y!.

So \(\displaystyle \frac{(y+ 2)!}{2!y!}= \frac{(y+2)(y+1)}{2}= 21\).

Does \(\displaystyle y^2+ 3y+ 2= 42\), \(\displaystyle y^2+ 3y= 40\) have any integer solutions?

 

[malcolmmalcolmm]

So it means if there is a person probabilty of him/her bein positive is 1/695
and probabilty of him/her bein negative is 1/295?

You seem to be misunderstanding the purpose of this site. We help you with math problems, not do them for you! And to do that it helps to know what you already understand about a problem and what you can already do.

Here's how I would think about the third problem:


Imagine a population of 1000. 70%, 700, have the disease, 300 do not. Of the 700 who have the disease, 5%, 35, test negative, the other 665 test positive. Of the 300 who do not have the disease, 10%, 30, test positive, the other 270 test negative.

So a total of 665+ 30= 695 test positive of whom 665 actually have the disease.

Can you finish?

 

[pka]

Can you solve \(\dfrac{(R+2)!}{2!\cdot R!}=21~?\)

\(\dfrac{(R+2)!}{2!\cdot R!}=\dfrac{(R+2)(R+1)R!}{2!R!}=21\\R^2+3R+2=42\\R^2+3R-40=0\\(R+8)(R-5)=0\\\therefore\text{Red}=5\)