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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.
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.