Question

Shortly before midnight, on April 14, 1912, the Titanic collided with an iceberg and sank.

Out of the 2249 passengers, 1514 died that night. The passengers’ summarized data are shown below:

	1st Class	2nd Class	3rd Class	Crew	Total
Survived	209	125	183	218	735
Died	127	174	536	677	1514
	336	299	719	895	2249

(Round all answers to four decimals)

Suppose a passenger is selected at random:

a) What is the probability that the passenger survived?   

b) What is the probability that the passenger was in 3rd class?

          

c) What is the probability that the passenger survived and was a crew member?

d) What is the probability that the passenger was not in 1st class?

e) “Surviving” is  (Click to select)  dependent  disjoint  independent   mutually exclusive  of “being in 1st class”.

f) Suppose the passenger selected was in 2nd class. What is the probability that the passenger died?

g) What is the probability that a surviving passenger was a crew member?

h) What is the probability that the passenger survived or was a crew member?

i) “Surviving” and “being in 3rd class” are

Answer 1

Out of the 2249 passengers, 1514 died that night. The passengers’ summarized data are shown below:

	1st Class	2nd Class	3rd Class	Crew	Total
Survived	209	125	183	218	735
Died	127	174	536	677	1514
	336	299	719	895	2249

a) What is the probability that the passenger survived?   

Total passengers=2249

Total passengers survived = 735

Probability that the passenger survived = 735 / 2249 = 0.3268119

Thus required probability = 0.3268

b) What is the probability that the passenger was in 3rd class?

Total passengers in 3rd class = 719

Total passengers =2249

Probability that the passenger was in 3rd class = passengers in 3rd class / Total passengers

                                                                            = 719 /2249 = 0.3196976

Thus required probability = 0.3197

          

c) What is the probability that the passenger survived and was a crew member?

Crew member survived = 218

Total passengers=2249

Total passengers survived = 735

Probability that the crew member survived = Crew member survived/Total passengers

                                                                     = 218 / 2249 = 0.09693197

Thus Probability that the crew member survived from all passengers on boat = 0.0969

Probability that the crew member survived = Crew member survived/Total passengers survived

                                                                     = 218 / 735 = 0.2965986

Probability of survived crew member in all survived passengers = 0.2966

d) What is the probability that the passenger was not in 1st class?

Passenger in 1st class = 336

Total passengers=2249

Passenger was not in 1st class = Total passengers - Passenger in 1st class = 2249 - 336

                                                  = 1913

Probability that the passenger was not in 1st class = Passenger not in 1st class/ Total passengers

                                                                                 = 1913 / 2249 = 0.8506003

Thus required probability = 0.8506