Survival probability of a passenger given that the passenger is a female staying in first class.

Question

This question is related to the Titanic incident:

What is the survival probability of a passenger given that the passenger is a female staying in first class?

Information:

• Number of people = 891
• Number of first class people = 216
• Number of second class people = 184

• Number of third class people = 491

• Number of first class female survivors = 91

• Number of first class female died= 3
• Number of first class male survivors = 45

• Number of first class male died= 77

• Number of second class female survivors = 70

• Number of second class female died= 6
• Number of second class male survivors = 17

• Number of second class male died= 91

• Number of third class female survivors = 72

• Number of third class female died= 72
• Number of third class male survivors = 47

• Number of third class male died= 300

• Number of females = 314

• Number of males = 577
• Number of females = 314
• Number of males = 577
• Number of females = 314
• Number of males = 577
• Number of survivors = 342
• Number of dead = 549
• Number of female survivors = 233
• Number of male survivors = 109

The solution is ~ 0.972222

I know that I need to use conditional probability on this question, however, I am not sure what should it look like.

I am not sure if I need to get the P(female), P(first class), P(female|first class), and then P(survivor|(female|first)).

Any clues would be appreciated.

Answer 1

Let's pull out the important information:

Number of first class female survivors = 91

Number of first class female died= 3

So, from this, we can ascertain that there was a total of $91+3=94$ first class female passengers.

Out of the 94 first class female passengers, 91 survived, giving a survival probability of $$\dfrac{91}{94} \approx 0.9680851$$

This is not quite the answer you were given, but this would be the correct answer given the data you provided.