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6. The table has data about the fate of passengers in the sinking of the Titanic ocean liner inDetermine each of the following: (4 x 2 = 8 marks)(a) P(not surviving first class)(b) P (not surviving in first class and not a man)(c) P (not surviving in second class and not a man)(d) P (not surviving in third class and not a man)(e) What conclusion (s) can you draw based on the above probabilities? Briefly explain youranswer (2 marks)

6. The table has data about the fate of passengers in the sinking of the Titanic ocean-example-1

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Answer:

• (a)P(not surviving | first class)=0.4061.

,

• (b)P (not surviving| in first class and not a man)= 0.0403.

,

• (c)P (not surviving| in second class and not a man)= 0.1121.

,

• (d)P (not surviving in third class and not a man)= 0.1159.

Explanation:

From the given information, the data is totalled in the table below:

(a) P(not surviving | first class)

• The total number of those in First Class = 293

,

• The number of those in First class who died = 114+4+1=119

Therefore:


P\left(\text{not surviving}|\text{ first class}\right)=(119)/(293)\approx0.4061

The probability of not surviving given that they are in first class is 0.4061.

(b) P (not surviving| in first class and not a man)

• The number of women and children in first class = 293-(114+55)=124

,

• The number of women and children who died = 4 + 1 =5


\text{ P \lparen not surviving\mid in first class and not a man\rparen}=(5)/(124)=0.0403

The probability of not surviving given that they are in first class and not a man is 0.0403.

(c)P (not surviving| in second class and not a man)

• The number of women and children in second class = 268-(139+13)=116

,

• The number of women and children who died = 13+0 = 13


\text{ P \lparen not surviving\mid in second class and not a man\rparen}=(13)/(116)\approx0.1121

The probability of not surviving given that they are in second class and not a man is 0.1121.

(d)P (not surviving in third class and not a man)

• The number of women and children who died in third class = 91+55=146

,

• The total number of passengers = 1260

Therefore:


\text{ P \lparen not surviving in third class and not a man\rparen}=(146)/(1260)\approx0.1159

The probability of not surviving in third class and not a man is 0.1159.

(e)Of the calculated probabilities, the probability of not surviving given that they are in first class is the highest.

6. The table has data about the fate of passengers in the sinking of the Titanic ocean-example-1
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