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:
C
Step-by-step explanation:
Given the logarithmic equation
First, notice that
So, there is no possible solutions, all possible solutions will be extraneous.
Solve the equation:
then
Hence, 
and 
are extraneous solutions
Answer: £5.39
Step-by-step explanation:
500g strawberries = 4.10
100 g = 0.82
300g = 2.46
400g raspberries = 7.46 - 2.46 = 5.00
100g = 1.25
300g = 3.75
200g strawberries = 0.82 * 2 = 1.64
3.75 + 1.64 = 5.39
What integer is less than 37 but greater than 35?
Answer: 33.85 mm
Step-by-step explanation:
Use trigonometry, tan equation
You are give the tan angle and adjacent side, you need to find the opposite side so
O
T A
Tan(72)= x/11
x= tan(72) x 11
x= 33.85
