A student takes a driving test until it is passed.
If the probability the test is passed on any attempt is 4/7 and if the attempts are independent, what is the probability the test is taken an even number of times?

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,

p = 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.

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.