Before they graduate from great lakes high school, all 12th grade students fill out a survey about their future college plans.
1. are you attending an in-state college after high school graduation?
2. will you begin college during the summer semester?
the same group of students questions recorded on the table above.
1. determine the probability college during the summer semester and attend an in-state college.
2. determine the probability that the student will begin college during the summer semester given that he’s attending it in state college.
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Step-by-step explanation:

Let represent the event that the student is attending an in-state college. Let represent the event that the student will be in college during the summer semester.

The first question is asking for the chance that the student will is attending an in-state college and will start during the summer semester. That probability can be written as .

is the intersection of the two events. On the table, the number of students that satisfy this condition is in the cell at the intersection of

There are students that satisfy the condition .

The probability in question one does not specify any "given" condition. The denominator of this probability will thus be the number of all students in this survey. Cells in this table are mutually exclusive and covers all students in the survey. There are thus students in this survey.

.

This question states the condition "given" that the student is attending an in-state college. In other words, that student needs to be chosen from the first column of students that are attending an in-state college.

The numerator will still be , the number of students that attend in-state colleges and begin college in the summer semester. However, the denominator will only be the sum of the two cells in the first column. That is: . The probability will be:

.