probability

In this problem, you are given descriptions in words of certain events (e.g., "at least one of the events A,B,C occurs"). For each one of these descriptions, identify the correct symbolic description in terms of A,B,C from Events E1-E7 below. Also identify the correct description in terms of regions (i.e., subsets of the sample space Ω) as depicted in the Venn diagram below. (For example, Region 1 is the part of A outside of B and C.)

Symbolic descriptions:

Event E1: A∩B∩C

Event E2: (A∩B∩C)c

Event E3: A∩B∩Cc

Event E4: B∪(Bc∩Cc)

Event E5: Ac∩Bc∩Cc

Event E6: (A∩B)∪(A∩C)∪(B∩C)

Event E7: (A∩Bc∩Cc)∪(Ac∩B∩Cc)∪(Ac∩Bc∩C)

At least two of the events A, B, C occur.

Status: incorrect

Status: incorrect
At most two of the events A, B, C occur.

Status: incorrect

Status: incorrect
None of the events A, B, C occurs.

Status: incorrect

Status: incorrect
All three events A, B, C occur.

Status: incorrect

Status: correct
Exactly one of the events A, B, C occurs.

Status: incorrect

Status: incorrect
Events A and B occur, but C does not occur.

Status: incorrect

Status: correct
Either event B occurs or, if not, then C also does not occur.

Status: incorrect

Status: incorrect

  1. 👍 0
  2. 👎 0
  3. 👁 1,500
  1. At least two of the events A, B, C occur.
    Event E6
    Regions: 2 4 5 6

    At most two of the events A, B, C occur.
    Event E2
    Regions: 1 2 3 5 6 7 8

    None of the events A, B, C occurs.
    Event E5
    Region: 8

    All three events A, B, C occur.
    Event E1
    Region: 4

    Exactly one of the events A, B, C occurs.
    Event E7
    Regions: 1 3 7

    Events A and B occur, but C does not occur.
    Event E3
    Region: 2

    Either event B occurs or, if not, then C also does not occur.
    Event E4
    Regions: 1 2 3 4 6 8

    1. 👍 3
    2. 👎 0

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