In this the anniversary of the sinking of the Titanic, it is interesting to look at the distribution of those who survived, and those who died. The table below describes the number of men, women and children who were passengers on the Titanic. The table lists both the number who survived as well as the number in each category who died. Be aware of the components listed of males, and of females.

Titanic Mortality Data

Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
1692 422 64 45 2223

If we were to randomly select one passenger:

a. Find the probability that the selected passenger is male.
b. Find the probability that the selected passenger survived.
c. Given that the selected passenger is female, what is the probability that she died.
d. Given that the selected passenger survived, what is the probability that the passenger is male?
e. Find the probability that the selected passenger is male and died
f. Find the probability that the selected passenger survived or is female?
g. Are the events the selected passenger died and the selected passenger is male independent events? Explain.

Solution Preview

See attachment for table

a. Find the probability that the selected passenger is male.

Total No. of male = 1692 + 64 = 1756

P (the selected passenger is male) = Favourable No. of cases (f)/Total No. of cases (n) = 1756/2223
=0.7899

b. Find the probability that the selected passenger survived.

P (the selected passenger survived) = Favourable No. of cases (f)/Total No. of cases (n) = 706/2223
=0.3176

c. c. Given that the selected passenger is female, what is the probability that she died.

Let A and B respectively be the events that the selected passenger is female and the passenger died.

Total number of female = 422 + 45 = 467

Total ...

Solution Summary

The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.

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