SOLUTION: For a certain population we define the following events for mother’s age at time of giving birth: A=under 20 years; B=20 - 24 years; C=25 - 29 years; D=30 - 44 years. a-

Algebra ->  Probability-and-statistics -> SOLUTION: For a certain population we define the following events for mother’s age at time of giving birth: A=under 20 years; B=20 - 24 years; C=25 - 29 years; D=30 - 44 years. a-      Log On


   

Question 1186927: For a certain population we define the following events for mother’s age at time of
giving birth:
A=under 20 years; B=20 - 24 years; C=25 - 29 years; D=30 - 44 years.
a- Are the events A, B,C, and D pairwise mutually exclusive?
b-State in words the event E=(A∪B)
c-State in words the event F = (B∪C)
d-Comment on the event G =(A∩B)
e-Comment on the event H =(A∪(Dbar))
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's analyze the given events related to mother's age at birth:
**a. Are events A, B, C, and D pairwise mutually exclusive?**
**Yes.**
*Explanation:* Pairwise mutually exclusive means that no two events can occur at the same time. A mother cannot be both under 20 *and* between 20-24 years old at the same time. The age ranges are distinct and non-overlapping. Therefore, the events A, B, C, and D are pairwise mutually exclusive.
**b. State in words the event E = (A ∪ B)**
Event E represents the event that the mother is *under 25 years old* at the time of giving birth. (It's the union of the events "under 20" and "20-24").
**c. State in words the event F = (B ∪ C)**
Event F represents the event that the mother is *between 20 and 29 years old* (inclusive) at the time of giving birth. (It's the union of the events "20-24" and "25-29").
**d. Comment on the event G = (A ∩ B)**
Event G represents the intersection of events A and B. Since A and B are mutually exclusive (as discussed in part a), their intersection is the empty set. That is, it is impossible for a mother to be both under 20 and between 20 and 24 at the same time. So, G is the *null event* or *impossible event*. P(G) = 0.
**e. Comment on the event H = (A ∪ (Dᶜ))**
* Dᶜ (D complement or "D bar") represents the event that the mother is *not* between 30 and 44 years old. This includes mothers under 20, between 20-24 and 25-29. (It's the union of A, B, and C)
* H = (A ∪ (Dᶜ)) represents the union of event A (under 20) and the event (Dᶜ) (not between 30 and 44). Since A is already included within Dᶜ, H is equivalent to Dᶜ.
Therefore, event H represents the event that the mother is *not* between 30 and 44 years old at the time of giving birth (i.e., the mother is 29 or younger).