Nicholas J. answered • 08/03/15
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Duke University PhD; Math, Comp Sci, Econ; 10+ Years Experience
57% of students studied, which decomposes into
52% who both studied and saw an increase in their exam grade
5% who both studied and did Not see an increase in their exam grade
The percentages above are relative to the whole population of 100 students, to get the requested probability, recall that:
One way to find out the probability of an event is to
Take the ratio of the number of times the event happened, over the total number of times the event could have happened.
Total number of times the event happened:
52 = 52% of 100 students studied and saw an increase in their exam grade
Total number of times the event could have happened:
57 = 57% of 100 students studied
Adam D.
Nicholas,
I follow your answer section...
Probabilities:
P(raise in grade and studied) = 52/100 = 0.52
P(studied) = 57/100 = 0.57
But disagree with your comment section. I get the following...
Conditional probability:
P(raise in grade given studied) = P(raise in grade and studied)/P(studied) = (0.52)/(0.57) = 0.912
It looks like you conditioned the sample space for a student who saw a raise in grade. Meaning 0.897 is the probability that a student studied for the test given the student saw a raise in grade, that is 52/58. I bet this is just a simple mistake in your comment because the solution built up in your answer portion is right on! Hope this helps.
-Adam
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08/09/15
Nicholas J.
08/03/15