# Probability Distribution

Can you tell me if my calculations are correct?  Thanks.

The table to the right gives a breakdown of 2,153 civil cases that were appealed. The outcome of the​ appeal,  as well as the type of trial​

(judge or​ jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal and type of

trial are observed.

Jury      Judge      Totals
Plaintiff trial win-reversed            198      75      273
Plaintiff trial win-affirmed/dismissed      438      242      680
Defendant trial win-reversed            104      73      177
Defendant trial win-affirmed/dismissed      726      297      1023
Totals      1466      687      2153

The probability that a randomly selected case is a jury trial is ---> 4/1466

The probability that the final outcome of a randomly selected case is ​'defendant trial win is reversed​' is  ---> 104/1466

The probability that the final outcome of a randomly selected case is ​'defendant trial win is reversed​'  and that the case is a
jury trial is --> 4 / 1466

The probability that the final outcome of a randomly selected case is a defendant trial win given that the
case is a judge trial is ----> 4/687
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Commented:
I'm not getting the same answers. Maybe I'm missing something.

The total number of cases is 2153, so the chance that a randomly selected case is a jury trial should be 1466/2153, I would think,

Similarly, for the number of cases which are "defendent trial win reversed" should be 177/2153.

The probability that the final outcome of a randomly selected case is a defendant trial win given that the case is a judge trial is 297/687
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Author Commented:
Thanks.
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