#### Answer

a)0.8125
b)0.1875
c)0.03125

#### Work Step by Step

Data given :
Total number of students : 128
Number of students on the honor roll : 52
Number of students not on the honor roll : 128 - 52 = 56 (remaining)
Number of students on to college : 48 out of the 52 and 56 out of the 76 = 104
Number of students not on to college : 4 out of the 52 and 20 out of the 76 (remaining) = 24
a) We compute the probability that a student selected at random from the class is going to college (pick the total number of student going to college and the total number of students in the class).
Hence,
$P(E)=\frac{n(E)}{n(S)}=\frac{48+56}{128}=\frac{104}{128}=0.8125$
b) We will calculate the probability that a student selected at random from the class is not going to college (pick the total number of student not going to college and the total number of students in the class)
$P(E)=\frac{n(E)}{n(S)}=\frac{4+20}{128}=\frac{24}{128}=0.1875$
$P(E)=1-P(\bar{E})=1-0.8125=0.1875$
(Observation: We could have count the probability that a student selected at random from the class is not going to college by subtracting from 1 the probability that a student selected at random from the class is going to college)
c) We compute the probability of not going to college and on the honor roll (Number of students on the honor roll and not going to college are 52-48 = 4)
$P(E)=\frac{n(E)}{n(S)}=\frac{52-48}{128}=\frac{4}{128}=0.03125$