1. ## Basic Probablility

Hi everyone. I am a math tutor at a college and we don't have any tutors here today that have done stats, so I was wondering if you guys could take a look at this and give me a thorough explanation of how to do the following problem:

The data in the table are from the voyage of the Titanic and show the survivor rates broken down by class of passenger. Use the table to answer the questions below.

$\displaystyle \begin{tabular}{c|c|c|c|c|c} \null &\text{first} &\text{second}&\text{third}&\text{crew}&\text{Tota l}\\ \hline \text{Survived}&199 &119&174&214&706\\\text{Died}&130&166&536&685&1517 \\\text{Total}&359&285&710&899&2223 \end{tabular}$

Find the following:

1.$\displaystyle P(\text{surviving})$

2. $\displaystyle P(\text{surviving }|\text{ \null }1^{st}\text{ class passenger})$

3. $\displaystyle P(\text{surviving }|\text{ \null }3^{rd}\text{ class passenger})$

4. Are the events of Surviving and class of passenger independent? Justify your answer.

So, for 1., would it be $\displaystyle P(\text{surviving})=\frac{\text{number of survivors}}{\text{total number of passengers}}$;

For 2., $\displaystyle P(\text{surviving }|\text{ \null }1^{st}\text{ class passenger})=\frac{\text{number of first class survivors}}{\text{total number of passengers}}$;

for 3., $\displaystyle P(\text{surviving }|\text{ \null }3^{rd}\text{ class passenger})=\frac{\text{number of third class survivors}}{\text{total number of passengers}}$;

and, finally for 4., The events are dependent because those passengers in 1st class were (at that time in history) given the first option to board the lifeboats.

Okay, these answers are what I've come up with. Could someone please do the problem professionally and give a really good explanation along the way? I'm trying to learn stats so that I can better help the students enrolled in the course.

Thanks.

2. Originally Posted by VonNemo19
Hi everyone. I am a math tutor at a college and we don't have any tutors here today that have done stats, so I was wondering if you guys could take a look at this and give me a thorough explanation of how to do the following problem:

The data in the table are from the voyage of the Titanic and show the survivor rates broken down by class of passenger. Use the table to answer the questions below.

$\displaystyle \begin{tabular}{c|c|c|c|c|c} \null &\text{first} &\text{second}&\text{third}&\text{crew}&\text{Tota l}\\ \hline \text{Survived}&199 &119&174&214&706\\\text{Died}&130&166&536&685&1517 \\\text{Total}&359&285&710&899&2223 \end{tabular}$

Find the following:

1.$\displaystyle P(\text{surviving})$

2. $\displaystyle P(\text{surviving }|\text{ \null }1^{st}\text{ class passenger})$

3. $\displaystyle P(\text{surviving }|\text{ \null }3^{rd}\text{ class passenger})$

4. Are the events of Surviving and class of passenger independent? Justify your answer.

So, for 1., would it be $\displaystyle P(\text{surviving})=\frac{\text{number of survivors}}{\text{total number of passengers}}$;

For 2., $\displaystyle P(\text{surviving }|\text{ \null }1^{st}\text{ class passenger})=\frac{\text{number of first class survivors}}{\text{total number of passengers}}$;

for 3., $\displaystyle P(\text{surviving }|\text{ \null }3^{rd}\text{ class passenger})=\frac{\text{number of third class survivors}}{\text{total number of passengers}}$;

and, finally for 4., The events are dependent because those passengers in 1st class were (at that time in history) given the first option to board the lifeboats.

Okay, these answers are what I've come up with. Could someone please do the problem professionally and give a really good explanation along the way? I'm trying to learn stats so that I can better help the students enrolled in the course.

Thanks.
1. Correct

2. Denominator should be Number of 1st class passengers - because the conditional probability P(A|B)=$\displaystyle \frac{P(A and B)}{P(B)}$

3. Denominator should be Number of 3rd class passengers -same reason as at 2.

4. Test for independent events: A and B are independent if P(A and B) = P(A) * P(B) - apply the test for this case and see if the 2 events in your question pass it or not.