Answer:
A) P(A⋂B) = 0.35
B) P(A⋃B)= 0.53
C) P(A⋂B′) = 0.08
D) P(A|B) = 0.778
Step-by-step explanation:
We know the following from the question:
- Let Proportion of Americans who expect to save more money next year than they saved last year be
P(A) and its = 0.43
-Let proportion who plan to reduce debt next year be P(B) and it's =0.81
A) probability that this person expects to save more money next year and plans to reduce debt next year which is; P(A⋂B) = 0.43 x 0.81 = 0.348 approximately 0.35
B) probability that this person expects to save more money next year or plans to reduce debt next year which is;
P(A⋃B)= P(A) + P(B) − P(A⋂B)
So, P(A⋃B)= 0.43 + 0.45 − 0.35 = 0.53
C). Probability that this person expects to save more money next year and does not plan to reduce debt next year which is;
P(A⋂B′) = P(A) − P(A⋂B)
P(A⋂B′) =0.43 − 0.35 = 0.08
D) Probability that this person does not expect to save more money given that he/she does plan to reduce debt next year which is;
P(A|B) = [P(A⋂B)] / P(B)
So P(A|B) =0.35/0.45 = 0.778
Answer: False
Natural numbers are not closed under division
Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.
However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.
A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.
If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.