Before they graduate from Great Lakes High School, all 12th-grade students fill out a survey about their future college plans.
Are you attending an in-state college after high school graduation?
Will you begin college during the summer semester?
The same group of students is asked to answer yes or no to both questions. The students’ responses were recorded in the table below.
Attending an
In-State
College Not Attending
an In-State
College
Begin Summer
Semester 178 21
Won't Begin
Summer
Semester 301 162
Determine the probability that a student will begin college during the summer semester and attend an in-state college.
Determine the probability that a student will begin college during the summer semester given that he is attending an in-state college.
I DONT REALLY KNOW!!! LOL;)
To determine the probability that a student will begin college during the summer semester and attend an in-state college, we need to use the concept of conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that a student will begin college during the summer semester, given that they are attending an in-state college.
To calculate the conditional probability, we need to divide the number of favorable outcomes (students who begin college during the summer semester and attend an in-state college) by the total number of outcomes (all students attending an in-state college).
From the given information in the table, we can see that there are 178 students who answered "Yes" to attending an in-state college and beginning the summer semester.
To find the total number of students attending an in-state college, we need to add the number of students who attend an in-state college and begin the summer semester to the number of students who attend an in-state college and do not begin the summer semester.
So, the total number of students attending an in-state college is 178 + 21 = 199.
The probability that a student will begin college during the summer semester given that they are attending an in-state college is therefore 178/199.
To find this probability, divide the number of favorable outcomes (students who begin the summer semester and attend an in-state college, which is 178) by the total number of outcomes (students attending an in-state college, which is 199):
P(Begin summer semester | Attend in-state college) = 178/199.
Hence, the probability that a student will begin college during the summer semester and attend an in-state college is 178/199, and the probability that a student will begin college during the summer semester given that they are attending an in-state college is also 178/199.