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)
7.158 * 10^9 rounds to 7 * 10^9
7 * 10^9 = 7,000,000,000
Answer:
A = 3
Step-by-step explanation:
Given
(5x² + 3x + 4) - (2x² + 5x - 1)
Remove the parenthesis from the first and distribute the second by - 1
= 5x² + 3x + 4 - 2x² - 5x + 1 ← collect like terms
= 3x² - 2x + 5
In the form Ax² + Bx + C
with A = 3
Answer:
x1=6 , x2=1
Step-by-step explanation:
If you have any questions about the way I solved it,don't hesitate to ask
In order to graph the equation, you need some coordinates,
So, put x = 0,
2y = 6. y = 3. Coordinate = (0, 3)
Now, put y = 0,
-x = 6
x = -6 Coordinate (-6, 0)
In short, Just mark that two points and draw a line, graph is done
Hope this helps!
