probability

TITANIC: A Probability Case Study Name____________________________________

(4 points each)

The RMS Titanic:

On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table below. (Data source: http://www.encyclopedia-titanica.org/titanic-statistics.html)

	Survived	Did not survive	Total
First class passengers	201	123	324
Second class passengers	118	166	284
Third class passengers	181	528	709
Total passengers	500	817	1317

1. Calculate the following probabilities. Round your answers to three decimal places.

a. If one of the passengers is randomly selected, what is the probability that this passenger survived?

b. If one of the passengers is randomly selected, what is the probability that this passenger was in first class and survived?

c. If one passenger is randomly selected, what is the probability that the person is from 1st class or 3rd class?

d. If one passenger is randomly selected, what is the probability that the person is 2nd class or survived?

e. If two passengers are randomly selected (without replacement), what is the probability that both passengers are from 3rd class?

Gender and Class

Data on survival of passengers are summarized in the table below.

(Data source: http://www.encyclopedia-titanica.org/titanic-statistics.html)

	Survived	Did not survive	Total
Children in first class	4	1	5
Women in first class	139	4	143
Men in first class	58	118	176
Children in second class	22	0	22
Women in second class	83	12	95
Men in second class	13	154	167
Children in third class	30	50	80
Women in third class	91	88	179
Men in third class	60	390	450
Total passengers	500	817	1317

2. Find the following probabilities.

a. P(passenger survived given passenger was in first class)

b. P(passenger survived given passenger was in second class)

c. P(passenger survived given passenger was in third class)

d. P(passenger survived given passenger was a child)

e. P(passenger survived given |passenger was a woman)

f. P(passenger survived given passenger was a man)

g. P(child survived given child was in first class)

h. P(child survived given child was in second class)

i. P(child survived given child was in third class)

j. P(woman survived given woman was in first class)

k. P(woman survived given woman was in second class)

l. P(woman survived given woman was in third class)

m. P(man survived given man was in first class)

n.  P(man survived given man was in second class)

o. P(man survived given man was in third class)

3. Some believe that the rescue procedures favored the wealthier first class passengers. Other believe that the survival rates can be explained by the ”women and children first” policy. Investigate what might and might not be concluded from the given data. Use the data you found to back up any conclusions that you make.

a. In #2, what do the probabilities found in parts a through c suggest about class and survival?

b. In #2, what do the probabilities found in parts d through f suggest about survival and gender?

c. In #2, what do the probability found in parts g through i suggests about the survival of children in different classes?

d. In #2, what do the probability found in parts j through l suggests about the survival of women in different classes?

e. In #2, what do the probability found in parts m through o suggests about the survival of men in different classes?

https://www.illustrativemathematics.org/