High school mathematics probability formula, how can we correctly get the total number of probability? I'm always confused about the total number, so I want to know the formula about the total number

High school mathematics probability formula, how can we correctly get the total number of probability? I'm always confused about the total number, so I want to know the formula about the total number

According to the requirements, take all the situations into account. That is to count all the possible situations. Do more questions, you will have experience. Come on!
The best way, one by one!
Permutations are OK.
The formula of frequency, group distance and probability
Frequency: frequency / total
Group spacing: (: maximum number -- minimum number) / group number
Probability: the probability expressed by the result of theoretical calculation. Theoretically, the number of times of event a / the total number of events
The slope formula of straight line
The slope formula of straight line
What about y = ax + k?
If we know that the linear formula is ax + by + C = 0, then the slope = - A / b
If we know the coordinates of two points (x1, Y1) (X2, Y2), then the slope = (y2-y1) / (x2-x1)
How to deduce the formula of changing base of logarithmic function
It's how to push down logab = logcb / logca (a > 0 a is not equal to 1 c > 0 C is not equal to 1 b > 0)
Let P = log (a) B, q = log (c) A. then: B = a ^ P, a = C ^ Q
∴ b=a^p=(c^q)^p=c^(pq)
That is, log (a) b * log (c) a = log (c) B
∴ log(a)b=logcb/logca
logc(b) =x , logc(a) =y
c^x=b, c^y=a => c=a^(1/y)
=> a^(x/y) = c^x = b
=> loga(b) = x/y
If the slope of two intersecting lines is known, the formula for calculating the angle between them is given
Arrival angle formula
The angle from L1 to L2 is called the angle from L1 to L2. Tan θ = (k2-k1) / (1 + K1 · K2)
We need to add the absolute value upstairs
Derivation of formula for logarithmic function
log(a)(M^n)=nlog(a)(M)
Derivation of log (a) (n) = log (b) (n) / log (b) (a)
log(a)(M^n)
=Log (a) (m * m * m *.. m) (n m)
=Log (a) (m) + log (a) (m) + log (a) (m) +. + log (a) (m) (n logs (a) (m))
=nlog(a)(M)
log(a)(N)
=log(a)[b^log(b)(N)]
=log(b)(N) log(a)(b)
=log(b)(N) log(a)(a^log(b)(a))
=log(b)(N) / log(b)(a)
Let log (a) (m ^ n) = y,
Then a ^ y = m ^ n
M = a ^ (Y / N), substituting
nlog(a)(M)
=nlog(a)a^(y/n)
=n·y/n
=y.
∴log(a)(M^n)=nlog(a)(M) .
Log (a) (n) = log (b) (n) / log (b) (a)
Let t = log (a) (n),
Then a ^ t =... Expand
Let log (a) (m ^ n) = y,
Then a ^ y = m ^ n
M = a ^ (Y / N), substituting
nlog(a)(M)
=nlog(a)a^(y/n)
=n·y/n
=y.
∴log(a)(M^n)=nlog(a)(M) .
Log (a) (n) = log (b) (n) / log (b) (a)
Let t = log (a) (n),
Then a ^ t = n,
Take the logarithm of B as the base on both sides,
log(b)a^t=log(b)N,
t=log(b)(N) / log(b)(a).
∴log(a)(N)=log(b)(N) / log(b)(a).
Note: logarithmic formula is defined by exponential formula, so they are often interchanged
It can be seen that these two proofs are transformed into exponential form
Log (a) (m ^ n) = NLog (a) (m) is equivalent to a ^ (nlogam) = m ^ n
Log (a) (n) = log (b) (n) / log (b) (a) is equivalent to logb (n) = log (a) (n) log (b) (a)
Equivalent to B ^ [log (a) (n) * log (b) (a)] = n
That is, a ^ log (a) (n) = n
Obviously, it is true.
Slope formula of straight line and its application
It is known that a straight line passing through the origin o intersects the image of the function y = log8 x at two points m and N, and the parallel lines passing through the axes m and N intersect the image of the function y = log2 x at two points P and Q. are the points P, Q and the origin o on the same straight line? Please explain the reason
y=log(8)x=1/3*log(2)x
Let the linear equation be y = KX, and the intersection points (x1, kx1), (X2, kx2) of log (8) X
kx1=log(8)x1,kx2=log(8)x2
The parallel lines passing through M and N as y axis intersect with the image of function y = log (2) x at P and Q
Then the abscissa of P and Q are X1 and X2 respectively
The ordinates are
log(2)x1=3log(8)x1=3kx1,
log(2)x2=3log(8)x2=3kx2
So p (x1,3kx1), q (x2,3kx2)
The linear equation passing through P and Q is y = 3kx. Obviously, it also passes through the origin
So o, P and Q are collinear
How to deduce the formula of logarithm in logarithm function
How can we make better use of this formula and convert the logarithm of other bases into logarithm of base 10 or e
Log (a) B = log (s) B / log (s) a let log (s) B = m, log (s) a = n, log (a) B = R, then s ^ m = B, s ^ n = a, a ^ R = B, namely (s ^ n) ^ R = a ^ R = B, s ^ (NR) = B, so m = NR, namely r = m / N, log (a) B = log (s) B / log (s) a
The formula of the distance between a point and a straight line is obtained by the slope
It's not the following formula, which is the square of root a + the square of B. It's another formula expressed by slope. Please tell me what you know,
The distance from point a (m, n) to the straight line y = KX + B:
kx-y+b=0
Distance from point a to straight line: = | KM-N + B | / √ (k ^ 2 + 1 ^ 2)
Let a straight line equation be y = KX + B, a point a (x0, Y0) outside the line,
Distance from point to line:
d=|kx0+b-y0|/sqrt(1+k^2)
The detailed derivation method of the formula for finding the base of logarithmic function
log(c)(b)=x
log(c)(a)=y
b=c^x
a=c^y
log(a)(b)=log(c^y)(c^x)=x/y*log(c)(c)
So log (a) (b) = log (c) (b) / log (c) (a)