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:
[tex]P\left(\text{not surviving}|\text{ first class}\right)=\frac{119}{293}\approx0.4061[/tex]
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
[tex]\text{ P \lparen not surviving\mid in first class and not a man\rparen}=\frac{5}{124}=0.0403[/tex]
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
[tex]\text{ P \lparen not surviving\mid in second class and not a man\rparen}=\frac{13}{116}\approx0.1121[/tex]
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:
[tex]\text{ P \lparen not surviving in third class and not a man\rparen}=\frac{146}{1260}\approx0.1159[/tex]
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.
