Question 1184502
Let's revisit the problem of selecting 2 students from the group of 4 (Anna, Maria, Alex, Ivan) and calculate the probabilities.

**(a) Basic Outcomes and Probabilities:**

Here are the possible pairs of students the teacher can select (order doesn't matter):

*   AM (Anna, Maria)
*   AX (Anna, Alex)
*   AI (Anna, Ivan)
*   MX (Maria, Alex)
*   MI (Maria, Ivan)
*   XI (Alex, Ivan)

There are 6 possible outcomes. Since the selection is random, each outcome has an equal probability of 1/6.

**(b) Events A and B:**

*   **Event A ("at least one starts with A"):**  This event includes the outcomes where at least one of the selected students' names starts with "A".  The outcomes are:
    *   AM
    *   AX
    *   AI

    Therefore, P(A) = 3/6 = 1/2 = 0.5

*   **Event B ("at least one ends with a"):** This event includes the outcomes where at least one of the selected students' names ends with "a". The outcomes are:
    *   AM
    *   MX

    Therefore, P(B) = 2/6 = 1/3 ≈ 0.333

**(c) Combined Probabilities:**

*   **A ∪ B (A or B or both):** This is the event that at least one student's name starts with "A" *or* at least one student's name ends with "a" (or both). The outcomes are:
    *   AM
    *   AX
    *   AI
    *   MX

    Therefore, P(A ∪ B) = 4/6 = 2/3 ≈ 0.667

*   **A ∩ B (A and B):** This is the event that at least one student's name starts with "A" *and* at least one student's name ends with "a". The only outcome that satisfies both conditions is:
    *   AM

    Therefore, P(A ∩ B) = 1/6 ≈ 0.167