To solve this problem, we need to calculate the probability that the student will be absent two days in a row and then attend class on the third day.

Let's break down the problem step by step:

1. Day 1 (Given that the student attended the previous day): The probability that the student will be absent on the first day (denoted as $A_1$) is given as 0.04.

   $P(A_1) = 0.04$

2. Day 2 (Given that the student was absent on the first day): The probability that the student will be absent again on the second day (denoted as $A_2$) is 0.11, given that they were absent the previous day.

   $P(A_2 \mid A_1) = 0.11$

3. Day 3 (Given that the student was absent on both the first and second days): The probability that the student will attend on the third day (denoted as $T_3$) is the complement of the probability of being absent on the third day. That is, the probability of attending is $1 - 0.11 = 0.89$, given that they were absent the previous two days.

   $P(T_3 \mid A_2) = 0.89$

Overall Probability:

The total probability that the student will be absent for two consecutive days and attend on the third day is the product of the conditional probabilities:

$P(A_1 \cap A_2 \cap T_3) = P(A_1) \times P(A_2 \mid A_1) \times P(T_3 \mid A_2)$

Substituting the known values:

$P(A_1 \cap A_2 \cap T_3) = 0.04 \times 0.11 \times 0.89$

$P(A_1 \cap A_2 \cap T_3) = 0.003916$

Thus, the probability that the student will be absent for two consecutive days and then attend on the third day is 0.003916 or approximately 0.39%.

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Would you like further details or clarification?

Here are 5 related questions that expand on this topic:

1. What is the probability that the student will be absent for exactly one day?
2. How would the probability change if the student’s attendance pattern on a third day was different?
3. What is the probability that the student will attend all three days?
4. How would this scenario change if the initial attendance probability on day 1 was different?
5. How does this problem relate to Markov chains in probability theory?

Tip: When dealing with conditional probabilities, always check if the problem assumes dependence or independence between events!