Question

Q3: The following frequency table shows the classification of 90 students in their sophomore year of college according to their understanding of physics, chemistry and mathematics.

If a student is selected at random, find the probability that the student has

a) an extensive understanding of chemistry;

b) an extensive understanding of physics and an average understanding of mathematics and chemistry;

c) an extensive understanding of any two subjects and an average understanding of the third;

d) an extensive understanding of any one subject and an average understanding of the other two.

Q4: Refer to Q3. Given that a student, selected at random, is found to have an extensive understanding of physics, what is the probability that the student has
a) an extensive understanding of chemistry;
b) an extensive understanding of both chemistry and mathematics;
c) an extensive understanding of either chemistry or mathematics.

Answer 1

Q3)

a)P(extensive understanding of chemistry)=(16+4+18+4)/90=42/90=0.4667

b)P(extensive understanding of physics and average understanding or mathematics and chemistry)

=12/90=0.1333

c)P(extensive of two and average of third)=P(extensive of physics,chemistry and average of math)+P(extensive of physics,math and average of chemistry)+P(extensive of chemistry,math and average of physics)

=(18/90)+(14/90)+(4/90)=36/90 =0.4

d)

P(average of two and extensive of third)=P(average of physics,chemistry and extensive of math)+P(average of physics,math and extensive of chemistry)+P(average of chemistry,math and extensive of physics)=(14/90)+(16/90)+(12/90)=0.4667

4)

a)P(extensive in chemistry|extensive in physics)=(18+4)/(18+4+12+14)=22/48 =0.4583

b)P(extensive in chemistry and math|extensive in physics)=4/(18+4+12+14)=4/48=0.0833

c)P(extensive in chemistry or math|extensive in physics)=(18+4+14)/(18+4+12+14)=36/48=0.75

Answer 2

Are you sure About 4C? Because it said EITHER, Dose not that exclude having both the courses (C and M) extensive? I am saying the the four should not be count. Therefore, it should be 32/48. 
I am not sure, but that is my guess.

Answer 3

I am anon, I have checked with my insructor and answer #1 is correct. Either include any of the two or both. Sorry.