Question 1196670
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The notation P(A | B) means "P(A) given event B happened"
We could write like "P(A given B)"


So asking something like P(survived | first class) means we know the person is in first class.
Since we can rewrite it as P(Survived given they are in first class)
There are 220+123 = 343 such people in first class.


Of this group of 343 people, 220 survived.


Therefore, 220/343 = <font color=red>0.641 approximately</font> is the probability of a survivor given they are in first class.


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We do the same thing for parts 2 through 4. 
I'll do the second part and leave parts 3 and 4 for you to do on your own. 


P(survived given second-class) = (number of second-class survivors)/(number of people in second-class)
P(survived given second-class) = (114)/(114+171)
P(survived given second-class) = 114/285
P(survived given second-class) = <font color=red>0.4 exactly</font>


You could write that as 0.400 or leave it as 0.4


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The last part of your question is garbled and missing important info.


You wrote "given that a passenger ____, what is the probability they had a ____ class ticket" but forgot to fill in those blanks


I'll go over an example


Question:  given that a passenger <u> &nbsp;&nbsp;survived&nbsp&nbsp</u>, what is the probability they had a <u> &nbsp;&nbsp;first&nbsp&nbsp</u> class ticket?


Solution:
There are 713 total survivors, which is the total of everything along row one (ignore the 713 in that row since it's the result of adding everything else)
220+114+174+205 = 713


There are 220 survivors from first class (upper left corner)


The probability we get is therefore 220/713 = 0.309 approximately


If we know for certain the person is a survivor, then there's a 30.9% chance they are from first class.


Once again, this answer applies to a hypothetical example since I don't know what the full original question was. But you'll use this example template to answer your specific question. 
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