Can someone double check my probablity problems please?! :)

noname1234

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Apr 1, 2006
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12
1. You have ingridients to make different types of iced tea: unsweetened, sweetened with sugar, artifical sweetener, flavored with lemon, mint or raspberry, caffeinated or decaffeinated. How many different kinds of tea can you make?

My answer: 18

2. The chess club has 12 members. If a team of 4 is to be selected, in how many different ways can the team be made?

My answer: 495

3. In the innner city of a metropolitan area, 500 robbers and 1500 assaults were reported. Of the robberies, 374 were committed by a stranger, and 126 by a person known to the victim. Of the assults, 827 were perpetrated by a stranger, and 673 by someone known to the victim. If one of the crim victims is selected at random, what is the probablity of the choice being a robbery victim, give that the criminal was an acquaintance of the victim?

My answer: ???

4. A new anti-depression drug causes side effects in 3.5% of the patient usin it. If tihs drug is prescribed for 700 patients, what are the mean of the number of patients that will experience side effects?

My answer: 24.5
 
1,2, & 4 are correct.

#3 \(\displaystyle \L
\begin{array}{cccc}
{} & A & R & {} \\
\hline
N & {673} & {126} & {799} \\
S & {827} & {374} & {1201} \\
\hline
{} & {1500}& {500}{} \\
\end{array}\) so 126/799.
 
Think about!
There are 799 who are known to the victim.
126 of those did robberies.
That why we make a table.
 
Re: Can someone double check my probablity problems please?!

Hello, noname1234!

I used Bayes' Theorem on #3 and got the same answer . . .

3. In the innner city of a metropolitan area, 500 robberiess and 1500 assaults were reported.
Of the robberies, 374 were committed by a stranger, and 126 by a person known to the victim.
Of the assults, 827 were perpetrated by a stranger, and 673 by someone known to the victim.

If one of the victims is selected at random, what is the probablity of the choice being a robbery victim,
given that the criminal was known to the victim?
Bayes' Theorem says: \(\displaystyle \:p(\text{robbery }|\text{ known}) \;=\;\L\frac{P(\text{robbery }\cap\text{ known})}{P(\text{known})}\)

\(\displaystyle P(\text{robbery})\:=\:\frac{500}{2000}\:=\:\frac{1}{4}\)
\(\displaystyle P(\text{robbery }\cap\text{ known})\:=\:\frac{1}{4}\cdot\frac{126}{500}\;=\;\frac{378}{6000}\)

\(\displaystyle P(\text{assualt})\:=\:\frac{1500}{2000}\:=\:\frac{3}{4}\)
\(\displaystyle P(\text{assault }\cap\text{ known})\:=\:\frac{3}{4}\cdot\frac{673}{1500}\:=\:\frac{2019}{6000}\)

Hence: \(\displaystyle \:p(\text{known})\:=\:\frac{378}{6000}\.+\,\frac{2019}{6000}\:=\:\frac{2397}{6000}\)

Therefore: \(\displaystyle \:p(\text{robbery }|\text{ known})\:=\:\L\frac{\,\frac{378}{6000}\,}{\frac{2397}{6000}}\;=\;\frac{378}{2397}\;=\;\frac{126}{799}\)


pka's method is more logical and certainly faster!
 
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