MHB Practice test help - probability from data

[CosmoK123456]

Having some trouble with this. I think the answer to question 1 is 26% and question 2 is 2%. I'm not sure when to divide by 163 or 100??
practice test help:
About 26% of orthopedic surgeries involves knee problems. The following table summarizes data collected from a sample of adults who have knee surgery. (Source: American Academy of Orthopedic Surgeons)

age, full knee replacement, no knee replacement
18-44,2, 9
45-64,25, 11
65-74,43,27
75-84, 27, 14
85-older,3, 2 1) What is the probability that an orthopedic surgical case selected at random involves
knee surgery?

2) What is the probability that a person from ages 18 – 44 who has knee surgery has a
full knee replacement?

3) What is the probability that a person from 45 – 64 who has knee surgery has a full
knee replacement?

4) What is the probability that a person who has knee surgery has a full knee
replacement?

 

[I like Serena]

Welcome to MHB, CosmoK! :)

Having some trouble with this. I think the answer to question 1 is 26% and question 2 is 2%. I'm not sure when to divide by 163 or 100??
practice test help:
About 26% of orthopedic surgeries involves knee problems. The following table summarizes data collected from a sample of adults who have knee surgery. (Source: American Academy of Orthopedic Surgeons)

[TD="align: center"]age[/TD]
[TD="align: center"]full knee replacement[/TD]
[TD="align: center"]no knee replacement[/TD]

[TD="align: center"]18-44[/TD]
[TD="align: center"]2[/TD]
[TD="align: center"]9[/TD]

[TD="align: center"]45-64[/TD]
[TD="align: center"]25[/TD]
[TD="align: center"]11[/TD]

[TD="align: center"]65-74[/TD]
[TD="align: center"]43[/TD]
[TD="align: center"]27[/TD]

[TD="align: center"]75-84[/TD]
[TD="align: center"]27[/TD]
[TD="align: center"]14[/TD]

[TD="align: center"]85-older[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]2[/TD]

1) What is the probability that an orthopedic surgical case selected at random involves
knee surgery?

2) What is the probability that a person from ages 18 – 44 who has knee surgery has a
full knee replacement?

3) What is the probability that a person from 45 – 64 who has knee surgery has a full
knee replacement?

4) What is the probability that a person who has knee surgery has a full knee
replacement?

You have question 1 correct.

For question 2 and following, you need to know that the probability that something occurs, is the number of occurrences divided by the total number of occurrences.
In a formula:
$$\text{probability on event} = \frac{\text{number of occurrences of event}}{\text{total number of occurrences}}$$
The catch is that in your case the total number is the total number within a certain category.

Applied to question 2, you have:
\begin{aligned}
P &= \frac{\text{number of persons from ages 18 – 44 who have knee surgery who also have a
full knee replacement}}{\text{total number of persons from ages 18 – 44 who have knee surgery}} \\
&= \frac{2}{2 + 9} \\
&= \frac{2}{11} \\
&\approx 18\%
\end{aligned}

Perhaps you can apply it to questions 3 and 4?

EDIT: Fixed to 18% as Prove It remarked.

 

[Prove It]

Welcome to MHB, CosmoK! :)
You have question 1 correct.

For question 2 and following, you need to know that the probability that something occurs, is the number of occurrences divided by the total number of occurrences.
In a formula:
$$\text{probability on event} = \frac{\text{number of occurrences of event}}{\text{total number of occurrences}}$$
The catch is that in your case the total number is the total number within a certain category.

Applied to question 2, you have:
\begin{aligned}
P &= \frac{\text{number of persons from ages 18 – 44 who have knee surgery who also have a
full knee replacement}}{\text{total number of persons from ages 18 – 44 who have knee surgery}} \\
&= \frac{2}{2 + 9} \\
&= \frac{2}{11} \\
&\approx 22\%
\end{aligned}

Perhaps you can apply it to questions 3 and 4?

\displaystyle \frac{2}{11} \approx 18\%, not 22%...