Five hundred first-year students at a state university were classified according to both high school GPA and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.
High School GPA
Probation 2.5 to
< 3.0 3.0 to
< 3.5 3.5 and
above Total
Yes 50 55 30 135
No 35 135 195 365
Total 85 190 225 500
(a)
Construct a table of the estimated probabilities for each GPA-probation combination.
High School GPA
Probation 2.5 to
< 3.0 3.0 to
< 3.5 3.5 and
above Total
Yes
No
Total
(b)
Use the table constructed in part (a) to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester.

(c)
What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above?

(d)
Are the two events selected student has a high school GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent events? How can you tell?
Since
P(GPA 3.5 or above and probation) =
and
P(GPA 3.5 or above) ✕ P(probation) = ,
the two events are .