Answer:
The probability that the test is taken an even number of times is 0.30.
Step-by-step explanation:
The probability that a student passes the driving test at any attempt is, 
<em>p</em> = 4/7.
The event of a student passing in any attempt is independent of each other.
The probability that the test is taken an even number of times is:
P (even number of tests) = P (Passing in the 2nd attempt) 
                                                   + P (Passing in the 4th attempt)
                                                        + P (Passing in the 6th attempt) ...
If a student passed in the 2nd attempt it implies that he failed in the first.
Then,  P (Passing in the 2nd attempt) = 
Similarly, P (Passing in the 4th attempt) =  , since he failed in the first 3 attempts.
, since he failed in the first 3 attempts.
And so on.
Compute the probability of an even number of tests as follows:
P (even number of tests) = 
The result follows a Geometric progression for infinite values.
The sum of infinite GP is:

The probability is:
 P (even number of tests) = 
                                           
Thus, the probability that the test is taken an even number of times is 0.30.