The addition formula of ABCD four event probability P（A+B+C)=pA+pB+pC-pAB-pAC-pBC+pABC

The addition formula of ABCD four event probability P（A+B+C)=pA+pB+pC-pAB-pAC-pBC+pABC

This is the general rule of addition, the general writing as shown in the figure

Can we use probability addition formula to prove whether two events are mutually exclusive? Why not? Why?
Because P (a + b) = P (a) + P (b) - P (AB), if P (AB) = O, directly P (a + b) = P (a) + P (b), then on the other hand, can p (a + b) = P (a) + P (b) be used to prove that two events a and B are mutually exclusive? I seem to remember that they can't, but I forget why they can't? It seems to be possible to watch directly~

No, the key problem is: zero probability event can not be said to be impossible, a and B mutually exclusive requires that the product event AB is impossible, but p (AB) = 0 can not get the impossible conclusion (consider continuous random variables)

Probability addition formula
The addition formula, for any two events a and B, P (A and b) = P (a) + P (b) - P (AB) holds. If AB is an independent event, P (AB) = P (a) P (b), how do I feel that when AB is independent, P (A and b) = P (a) + P (b), the latter P (AB) does not need to be reduced

P (A and b) = P (a) + P (b) - P (AB) is for any event a and B,
When a and B are independent events, P (AB) = P (a) P (b) = 0, so p (A and b) = P (a) + P (b)

Fill in the appropriate numbers in the brackets to make the equation hold 0.56 * () + 0.44 * () - () = 0

0.56 × 0 + 0.44 × 0-0 = 0 or 0.56 × 1 + 0.44 × 1-1 = 0 or 0.56 × (- 1) + 0.44 × (- 1) - (- 1) = 0

Don't repeat
No decimals
No equations
Add, subtract, multiply and divide
It's better to multiply two digits by one digit or three digits by one digit

What are the differences between special relativity and general relativity? What are their core contents

General relativity is a theory of gravitation based on geometric language, which integrates special relativity and Newton's law of universal gravitation. It changes gravitation to describe the curved space-time caused by matter and energy in space-time, replacing the traditional view that gravitation is a force

Ask 200 oral arithmetic questions in Grade 5)

1.45+15×6= 135
2.250÷5×8=400
3.6×5÷2×4=60
4.30×3+8=98
5.400÷4+20×5= 200
6.10+12÷3+20=34
7.(80÷20+80)÷4=21
8.70+(100-10×5)=120
9.360÷40= 9
10.40×20= 800
11.80-25= 55
12.70+45=115
13.90×2= 180
14.16×6= 96
15.300×6= 1800
16.540÷9=60
17.30×20= 600
18.400÷4= 100
19.350-80= 270
20.160+70=230
21.18-64÷8= 10
22.42÷6+20=27
23.40-5×7= 5
24.80+60÷3=100
25.41+18÷2= 50
26.75-11×5= 20
27.42+7-29= 20
28.5600÷80=70
29.25×16= 400
30.120×25= 3000
31.36×11= 396
32.1025÷25=41
33.336+70= 406
34.25×9×4= 900
35.200-33×3= 101
36.3020-1010=2010
37.12×50= 600
38.25×8= 200
39.23×11= 253
40.125÷25=5
41.4200-2200=2000
42.220+80= 300
43.20×8×5= 800
44.600-3×200=0
45.20+20÷2= 30
46.35-25÷5= 30
47.36+8-40= 4
48.2800÷40=70
49.98÷14 = 7
50.96÷24 = 4
51.56÷14 =4
52.65÷13 = 5
53.75÷15 = 5
54.120÷24 =5
55.200÷25 = 8
56.800÷16 = 50
57.840÷21 =40
58.560÷14 = 40
59.390÷13 = 30
60.600÷15 =40
61.72÷24 = 3
62.85÷17 = 5
63.90÷15 =6
64.96÷16 = 6
65.78÷26 = 4
66.51÷17 =3
67.80÷40 = 2
68.100÷20 = 5
69.100÷4 =25
70.240÷40 = 6
71.920÷4 = 230
72.300÷60=5
73.64÷2 = 32
74.64÷4 = 16
75.50÷5 =10
76.60÷8 = 7.5
77.96÷4 = 24
78.90÷6 =15
79.400+80 = 480
80.400-80 = 320
81.40×80 =3200
82.400÷80 = 5
83.48÷16 = 3
84.96÷24 =4
85.160×5= 800
86.4×250= 1000
87.0×518= 0
88.10×76= 760
89.36×10=360
90.15×6= 90
91.24×3= 72
92.5×18= 90
93.26×4= 74
94.7×15=105
95.32×30= 960
96.40×15= 600
97.60×12= 720
98.23×30= 690
99.30×50=1500
100.5×700=3500

A problem of special relativity
It takes 10 seconds for a person to run 100 meters. On an object moving at 0.6 times the speed of light, observe how far the person has moved from the starting point to the end of the runway

It's all 100 meters, but the time is different. If you are a runner with your back to the runner, the time will be longer and vice versa. You can see that the time for him to run to the finish line is 10 seconds. After this happens, you can see that the light will reach your eyes, you can run straight ahead, you can catch up with you, and you can see it when the light catches up with you
0.6 by 10 seconds can run 18W km ah, think all to space

Who can give me 600 mental arithmetic questions
It's just oral arithmetic. Is it very useful and urgent?

The difference between general relativity and special relativity

Relativity is divided into general relativity and special relativity
The basic concept of general relativity is explained as follows
General relativity is the theory of relativity of gravitational field put forward by Einstein in 1913 after special relativity. This theory is completely different from Newton's theory of gravitation. It attributes the gravitational field to the bending of space-time around the object, and the motion of the object under the action of gravitation to the free motion of the object along the geodesic line in the bending space-time, General relativity, also known as spatiotemporal geometric dynamics, attributes gravity to the geometric properties of space-time
How to understand the space-time curvature of general relativity? Here we use a model analogy to explain. If there are two steel balls with large mass, according to Newton's view, they will be close to each other because of the mutual attraction of universal gravitation. Einstein's general relativity does not think that there is an attraction between the two steel balls. The reason why they are close to each other is that they are close to each other, The reason is that when there is no steel ball, the surrounding space-time is like a flattened net. Now two steel balls bend the net, so the two steel balls roll together along the curved net. This is equivalent to the movement of objects along the geodesic due to the bending of space-time. Therefore, Einstein's general theory of relativity is a theory of gravity without "gravity"
Furthermore, the theory is based on the two basic hypotheses of equivalence principle and generalized covariance principle. The equivalence principle is based on the fact that the mass of inertia and gravity of an object are equal. It is considered that gravity and inertial force in acceleration system are equivalent, and they are indistinguishable in principle. The generalized covariance principle can be regarded as a mathematical expression of the equivalence principle, That is to say, all the differential equations reflecting the laws of physics should keep the same form in all the reference frames. It can also be said that all the reference frames are equal, thus breaking the special status of inertial frame in special relativity. Because of the arbitrariness of the selection of reference frame, it is named general relativity
We know that Newton's law of universal gravitation holds that all objects with mass attract each other, which is a static over distance action
In general relativity, the law of gravitational field produced by matter is expressed by Einstein's field equation. The gravitational action reflected by it is dynamic and transmitted by the speed of light
General relativity is a more general theory than Newton's theory of gravitation. Newton's theory of gravitation is only the weak field approximation of general relativity. The so-called weak field means that the gravitational energy of an object in the gravitational field is far less than the inherent energy, and the difference between the two is shown in the force field. At this time, general relativity must be applied to correctly deal with the problem of gravitation
After the establishment of general relativity in 1915, Einstein proposed that its correctness can be tested from three aspects, namely, the so-called three major experimental verifications. These are the deflection of light near the sun, the precession of mercury perihelion and the frequency shift of spectral lines in the gravitational field. These were soon confirmed by the experimental observations at that time. Later, someone designed the radar echo time delay experiment, In the 1960s, a series of new discoveries in astronomy, such as 3K microwave background radiation, pulsars, quasars, X-ray sources and other new astrophysical observations, strongly supported general relativity, thus making people's interest in general relativity turn from cold to hot, It has become a hot frontier in physics
Einstein always regarded general relativity as the most important scientific achievement in his life. He said, "if I didn't find special relativity, someone else would find it. The problem is mature. But I think general relativity is different." indeed, general relativity contains more profound ideas than special relativity, This brand-new theory of gravity is still the best theory of gravity. Without bold spirit of innovation, indomitable perseverance, keen theoretical intuition and solid mathematical foundation, it is impossible to establish general relativity. The great scientist Thomson once called general relativity one of the greatest achievements in human history
Special relativity is
Special relativity is a theory based on the four-dimensional space-time view. To understand the content of relativity, we need to have a general understanding of the space-time view of relativity. In mathematics, there are various multi-dimensional spaces, but so far, the physical world we know is only four-dimensional, that is, three-dimensional space plus one-dimensional time, There is no discussion here
Four dimensional space-time is the lowest dimension of the real world. Our world happens to be four-dimensional. As for the high-dimensional real space, at least now we can't perceive it. A ruler rotates in three-dimensional space (excluding time), its length remains unchanged, but when it rotates, its coordinate values change, and there is a connection between the coordinates. The meaning of four-dimensional space-time is that time is the fourth dimensional coordinate, It is related to space coordinate, that is to say, space-time is a unified and indivisible whole
In four-dimensional space-time, mass (or energy) is actually the fourth dimension component of four-dimensional momentum. Momentum is the quantity describing the motion of matter, In addition, in the four-dimensional space-time, four-dimensional velocity, four-dimensional acceleration, four-dimensional force and four-dimensional form of electromagnetic field equations are also defined. It is worth mentioning that the four-dimensional form of electromagnetic field equations is more perfect, completely unifying electricity and magnetism, The electric field and magnetic field are described by a unified electromagnetic field tensor. The physical law of four-dimensional space-time is much more perfect than the three-dimensional law, which shows that our world is indeed four-dimensional. It can be said that at least it is much more perfect than Newton's mechanics. At least because of its perfection, we can't doubt it
In the theory of relativity, time and space form an inseparable whole - four-dimensional space-time, and energy and momentum form an inseparable whole - four-dimensional momentum. This shows that there may be a profound connection between some seemingly unrelated quantities in nature, There is also a deep connection between space-time and the four vectors of energy and momentum
There is no matter that doesn't move and there is no matter that doesn't move in the interaction. Because matter moves in the interaction, it is necessary to describe the motion in the relationship of matter, not in isolation. That is to say, the motion must be described