Final answer:
The probability that a student will miss at least one unannounced test during two absences is 9/25 (option B) , after calculating the complement of the probability of the student not missing any tests on those days.
Step-by-step explanation:
The question is asking for the probability that a student will miss at least one unannounced test if he is absent twice, given that the probability of a test being given during any class meeting is 1/5. To solve this, it's easier to first calculate the probability that the student will not miss any tests during the two absences, which is the complement of the desired probability.
Since the events are independent, the probability of the student not missing a test on a single day he is absent is 4/5 (the complement of 1/5). Therefore, the probability that he will not miss a test on both days he is absent can be calculated as (4/5) * (4/5) = 16/25.
The probability that he will miss at least one test can be found by subtracting this result from 1, which represents the total certainty of all possible outcomes:
1 - (16/25) = (25/25) - (16/25) = 9/25. So the correct answer is B. 9/25.