maths.....probability

The answer given by the above person is incomplete. he only gave the probability of passing at least one test, i.e., 3/4. However, he has not answered the probability of passing the road test, becasue passing at least one test can mean passing the theory test not the road test.
Here is the complete solution.
Probability of passing at least one test = 3/4 as calculated (not repeating here).
This is made up of three conditions:
(i) Passing both test=> probability = 2/3 * 1/4 = 1/6
(ii) Passing theory test and failing road test=> probability = 2/3 * 3/4 = 1/2
(iii) Failing theory test and passing road test=> probability = 1/3 * 1/4 = 1/12
(i) + (ii)+ (iii) = 1/6 + 1/2 + 1/12 = 3/4.
Thus, given that she passes at least one test [meaning one of the conditions (i), (ii) and (iii)] , the probability that shes passses the road test are actually (i) and (iii), thus it is equal to 1/6 + 1/12 = 1/4

Probability Jenny Pass the theory test = 2/3
Probability Jenny Fail the theory test = 1/3

Probability Jenny Pass the road test = 1/4
Probability Jenny Fail the road test = 3/4

Probability Jenny Fail both theory and road test = 1/3 x 3/4 = 1/4
Probability Jenny pass at least 1 part in the driving test = 1 - Probability Jenny Fail Both
= 1 - 1/4
= 3/4