SOLUTION: The Grand Prairie Charter School Admissions lottery in 2019 gave 130 admissions to incoming kindergartners. All applications needed to be completed by November 2019 to qualify for

Question 1187466: The Grand Prairie Charter School Admissions lottery in 2019 gave 130 admissions to incoming kindergartners. All applications needed to be completed by November 2019 to qualify for admission for the 2020 school year. Stanley Dev was one of the 815 children who entered this lottery. Let A = was given admission and let F = was a finalist.
Stanley’s chance of getting admitted into the school (in percentage terms, two decimal places) is
%.
In the December 2019, Stanley’s parents received a letter stating he was one of 225 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to get the admission, Stanley’s chance of getting the admission (in percentage terms, two decimal places) is
%.
Fill in “True” or “False”: A and F are not independent events.
Fill in “True” or “False”: A and F are mutually exclusive events.
Note: Show the work in your answer file on how you obtained the answer for the third and fourth questions. Guesswork will result in a penalty.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The first is 130/815 or 0.1595. or 0.16
The second is 130/225 or 0.578 or 0.58
P(A)*P(B)=P(A and B); P(A and B) means probability of being chosen in first*prob. in second is overall probability equals probability of getting both, which is 0.16*0.58 or 0.0928
the probability of making it overall is 130/815 or 0.16. This is not the same as 0.0928, so they are not independent. Indeed, what happens on the first does have a bearing on the second. If the first is not chosen, then there is no chance at all on the second, rather than a probability of 0.58. The answer is True, they are not independent.
They are not always mutually exclusive events. If they are chosen on the first, they may certainly be chosen on the second. The answer is False, they are not mutually exclusive events.

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