5) Use the diagram in C2. From the given figures we have 4 pieces of information:
- The probability of getting grade D only (implies a pass)=1/6
- The probability of not getting grade D (implies fail, or passing with a grade better than D)=5/6
- The probability of failing=1/9
- The probability of passing=8/9
Now let's define the regions X, Y, Z.
X probability of failing=1/9 (assuming that any grade below D is a fail; see (3) above)
Y probability of getting grade D=1/6 (see (1) above)
Z probability of getting better than grade D (we have to find)
X+Y=2/18+3/18=5/18, left circle (probability of failing or getting grade D)
Y+Z=probability of passing=8/9, right circle (see (4) above) so Z=8/9-1/6=13/18
X+Y+Z must equal 1 because it is certain that a student will pass or fail. And 1/9+1/6+13/18 does add up to 1. Also, (2) above is X+Z=1/9+13/18=15/18=5/6, so this fits, too.
Probability of getting a better grade than D is Z=13/18.