Answer:
<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>
By De morgan's law

which is Bonferroni’s inequality
<h3>Result 1: P (Ac) = 1 − P(A)</h3>
Proof
If S is universal set then

<h3>Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B) and P(A) ≥ P(B)</h3>
Proof:
If S is a universal set then:

Which show A∪B can be expressed as union of two disjoint sets.
If A and (B∩Ac) are two disjoint sets then
B can be expressed as:

If B is intersection of two disjoint sets then

Then (1) becomes

<h3>Result 3: For any two events A and B, P(A) = P(A ∩ B) + P (A ∩ Bc)</h3>
Proof:
If A and B are two disjoint sets then

<h3>Result 4: If B ⊂ A, then A∩B = B. Therefore P (A)−P (B) = P (A ∩ Bc) </h3>
Proof:
If B is subset of A then all elements of B lie in A so A ∩ B =B
where A and A ∩ Bc are disjoint.

From axiom P(E)≥0

Therefore,
P(A)≥P(B)
Answer:
Step-by-step explanation:
For this case we can define the random variable of interest as: "The nicotine content in a single cigarette " and for this case we know the following parameters:

And for this case we select a sample size of n =100 and we want to find the following probability:

And for this case we can use the z score formula given by:

And replacing we got:

And we can find the required probability with the normal standard table and we got:

Answer:
We know that ,

So ,

we can add 2 pi to it since there will be no change in the value
Also,

Answer : Option B
Answer:

Step-by-step explanation:
- t = time (in hours) → this is the independent variable
- s = total area cleaned (in square feet) → this is the dependent variable (as the number of square feet cleaned depends on the number of hours worked)
Therefore, if the rate of cleaning is 8 1/4 square feet per hour, the relationship between s and t is:

"Increased" means to add.
"Quotient" is a total of a division problem.
"A number" means the unknown.
This is our problem: 3 + 6 / N