probability is doing my head in

[mathnoob10]

hi, this is my 1st post here. i came across this site while googling for help. i always cant seem to get started. im worried about how to tackle these questions as im sure to get some in my exams. im not good with sentence questions either so how do i set this out?

heres the question im stuck on:


According to Link Resources, 16% of the U.S. population is technology-driven. However, these figures vary by region. For example, in the West the figure is 20% and in the Northeast the figure is 17% . Twenty-one percent of the U.S. population in general is in the West and 20% of the U.S. population is in the Northeast. Suppose an American is chosen randomly.

Round your answers to 3 decimal places.

a. What is the probability that the person lives in the West and is a technology-driven person?

b. What is the probability that the person lives in the Northeast and is a technology-driven person?

c. Suppose the chosen person is known to be technology-driven. What is the probability that the person lives in the West?

d. Suppose the chosen person is known not to be technology-driven. What is the probability that the person lives in the Northeast?

e. Suppose the chosen person is known to be technology-driven. What is the probability that the person lives in neither the West nor the Northeast?

 

[soroban]

Hello, mathnoob10!

Welcome aboard!

According to Link Resources, 16% of the U.S. population is technology-driven.
However, these figures vary by region.
For example, in the West the figure is 20% and in the Northeast the figure is 17%.
Twenty-one percent of the U.S. population is in the West and 20% is in the Northeast.

We can organize this data in a table.
(I hope you can see how the numbers are generated.)

. . \(\displaystyle \begin{array}{c||c|c|c||c|} & \text{West} & \text{Northeast} & \text{Other} & \text{Total} \\ \hline \hline \text{Tech} & 0.032 & 0.0272 & 0.1008 & 0.16 \\ \hline \sim\!\text{Tech} & 0.168 & 0.1428 & 0.5292 & 0.84 \\ \hline \hline \text{Total} & 0.20 & 0.17 & 0.63 & 1.00 \end{array}\)

Suppose an American is chosen randomly. (Round your answers to 3 decimal places.

(a) What is the probability that the person lives in the West and is a technology-driven person?

\(\displaystyle \text{From the table: }\(\text{West } \wedge \text{Tech}) \:=\:0.032\)

(b) What is the probability that the person lives in the Northeast and is a technology-driven person?

\(\displaystyle \text{From the table: }\(\text{NE} \wedge \text{Tech}) \:=\:0.0272\)

c. Suppose the chosen person is known to be technology-driven.
. . What is the probability that the person lives in the West?

\(\displaystyle P(\text{West} | \text{Tech}) \:=\:\frac{P(\text{West} \wedge \text{Tech})}{P(\text{Tech})} \;=\;\frac{0.032}{0.16} \;=\;0.20\)

(d) Suppose the chosen person is known not to be technology-driven.
. . What is the probability that the person lives in the Northeast?

\(\displaystyle P(\text{Northeast}\, | \sim\!\text{Tech}) \;=\;\frac{P(\text{Northeast}\, \wedge \sim\!\text{Tech})}{P(\sim\!\text{Tech})} \;=\;\frac{0.1428}{0.84} \;=\;0.17\)

e. Suppose the chosen person is known to be technology-driven.
. . What is the probability that the person lives in neither the West nor the Northeast?

\(\displaystyle P(\text{Other}\,|\,\text{Tech}) \;=\;\frac{P(\text{Other} \wedge \text{Tech})}{P(\text{Tech})} \;=\; \frac{0.1008}{0.16} \;=\;0.63\)

 

[hayden1haytch]

in the matrix why is the top left number 0.032? shouldn't it be 0.2X0.21 which is equal to 0.042?

 

[hayden1haytch]

these answers are wrong

 

[mathnoob10]

thanks soroban for your working out.

as hayden1haytch mentioned, your answers are incorrect, but using your layout and method i was able to successfully get the right answers.