probabilities

  

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. 
   1. If one of the passengers is randomly selected,       what is the probability that this passenger survived?
   2. If one of the passengers is randomly selected,       what is the probability that this passenger was in first class and       survived?
   3. If one passenger is randomly selected, what is       the probability that the person is from 1st class or 3rd class?
   4. If one passenger is randomly selected, what is       the probability that the person is 2nd class or survived?
   5. 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.

1. P(passenger survived      given passenger was in first class)
2. P(passenger survived      given passenger was in second class)
3. P(passenger survived      given passenger was in third class)
4. P(passenger survived      given passenger was a child)
5. P(passenger survived given |passenger was a woman)
6. P(passenger survived      given passenger was a man)
   
    
7. P(child survived given child was in first class)
8. P(child survived given child was in second class)
9. P(child survived given child was in third class)
10. P(woman survived given woman was in first class)
11. P(woman survived given woman was in second class)
12. P(woman survived given woman was in third class)
13. P(man survived given man was in first class)
14. P(man survived      given man was in second class)
15. 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. 

1. In #2, what do the probabilities found in parts a      through c suggest about      class and survival?
2. In #2, what do the probabilities found in parts d      through f suggest about      survival and gender?
3. In #2, what do the probability found in parts g through i suggests about the survival of children in different      classes?
4. In #2, what      do the probability found in parts j through l suggests about the survival      of women in different classes?
5. In #2, what      do the probability found in parts m through o suggests about the survival      of men in different classes?