Surviving the Titanic - Part 3

Since we know that women were more likely to survive the sinking of the Titanic than men, and we can see that the crew is predominantly composed of men, simply calculating the total survival rates for third class and crew gives a deceptive result:

Crew survival rate: $212 / 908 \approx 23.3\%$ Third class survival rate: $178 / 706 \approx 25.2\%$

However, if we look at each gender group individually, we can see a much clearer picture:

Women:

$\newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|l|c|c|c|} \hline \textbf{Group} & \textbf{Total} & \textbf{Saved} & \textbf{Survival Rate} \\\hline \text{Women, Third Class} & 165 & 76 & \mathbf{46.1\%} \\ \hline \text{Women, Crew} & 23 & 20 & \mathbf{87.0\%} \\ \hline \end{array}$

Men:

$\newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|l|c|c|c|} \hline \textbf{Group} & \textbf{Total} & \textbf{Saved} & \textbf{Survival Rate} \\\hline \text{Men, Third Class} & 462 & 75 & \mathbf{16.2\%} \\ \hline \text{Men, Crew} & 885 & 192 & \mathbf{21.7\%} \\ \hline \end{array}$

Thus we can see that the chances for survival were better for both men and women if they were members of the crew, even though the overall statistics hid that fact due to different distributions within the groups. This counter-intuitive result is known as Simpson's Paradox .

Given the above, the answer is clearly "Crew" .

Awesome problem!

I have never seen such an interesting paradox of this kind...

Being part of the Third Class, you would have 24,1% of the chance of being saved (not considering the children, which would make it higher). While being part of the Crew, you would have 23,4% of the chance of being saved.

Considering this, it's better to be on the Third Class...

But as you are a single person, man OR woman, the probability of being saved on each case is higher in the Crew then in the Third Class, what makes this problem so interesting!

What I think it's the most important fact is that by adding a new information (the gender), you change the decision to be taken.

Hello,since the question asked the survivality(either gender) whether as a crew or 3rd class passenger(adults),just that the % of survived ones,

For the crew(survived),

Male = (192 / 885) x 100% = 21.70%

Female = (20/23) x 100% =86.96%

For the 3rd class passengers,

Male = 75 / 462 x 100% = 16.23%

Female = 46.06%

As you can compare between those crews and 3rd class passengers,

you can see that higher survival chances are with the crews rather than 3rd class passengers,

therefore,be a crew to survive....

look for the lost list so that you can the ans.

Count the no. of saved people in crew and in third class.So, the group in which more people are saved, in that group only i have the more chance to be alive. So,the answer is crew....

JUST DIVIDE n. of total men of one category by its survivor and if there is greater result of one category than another then write the name o another category