Question

Problem 1. A total of 2,224 people sailed on the maiden voyage of the RMS Titanic, the second of the White Star Line’s Olympic-class ocean liners, from Southampton, England, to New York City. Partway through the voyage, the ship struck an iceberg and sank in the early morning of 15 April, 1912. Here are the mortality data of Titanic.

	Adult Men	Adult women	Boys	Girls
Survived	338	316	29	27
Died	1352	109	35	18

a. If an individual who was aboard the Titanic is randomly selected, what is the probability the individual is an adult man?

b. If an individual who was aboard the Titanic is randomly selected, what is the probability that the individual is an adult man, given that the selected person died?

c.What is the probability of getting a boy or a girl, given that the randomly selected person is someone who survived?

d. What is the probability of getting an adult man or an adult woman, given that the randomly selected person is someone who died?

Answer 1

	Adult Men	Adult Women	Boys	Girls	Total
Survived	338	316	29	27	710
Died	1352	109	35	18	1514
Total	1690	42	64	45	2224

Question (a)

Probability that the individual is an adult man = 1690 / 2224

= 0.759892

Question (b)

Probability that the individual is an adult man, given that the selected person died

Let the event Adult Man be A

Let the event Died be D

SO we need to find P(A | D)

P(A | D) = P(AD) / P(D)

P(AD) = 1352 / 2224

P(D) = 1514 / 2224

So P(A | D) = (1352 / 2224) / (1514 / 2224)

= 1352 / 1514

= 0.892999

Probability that the individual is an adult man, given that the selected person died = 0.892999

Question (c)

probability of getting a boy or a girl, given that the randomly selected person is someone who survived

We want P( BG | S) = P( (BG) S) / P(S)

S is the event that the individual is survived

P(S) = 710 / 2224

P( (BG) S) = Probability that a boy or girl has survived = 29/ 2224 + 27/ 2224 = 46 /2224

So P( BG | S) = (46 / 2224) / (710/2224)

= 46 / 710

= 0.064789

probability of getting a boy or a girl, given that the randomly selected person is someone who survived = 0.064789

Question (d)

probability of getting an adult man or an adult woman, given that the randomly selected person is someone who died

We want P(M W | D)

M being Adult Man, W being Adult Woman, D being Died

P(M W | D) = P ( (M W) D) / P(D)

P ( (M W) D) is the probability that the individual is either Adult Man or Adult Woman and has died

= (1352 / 2224) +(109 / 2224)

= 1461 / 2224

P(D) = 1514 / 2224

So P(M W | D) = (1461 / 2224) / (1514 / 2224)

= 1461 / 1514

= 0.964993

probability of getting an adult man or an adult woman, given that the randomly selected person is someone who died = 0.964993