Given:
The two way table.
To find:
The conditional probability of P(Drive to school | Senior).
Solution:
The conditional probability is defined as:
Using this formula, we get
...(i)
From the given two way table, we get
Drive to school and senior = 25
Senior = 25+5+5
= 35
Total = 2+25+3+13+20+2+25+5+5
= 100
Now,
Substituting these values in (i), we get
Therefore, the required conditional probability is 0.71.
Answer:
The Taylor series of f(x) around the point a, can be written as:
Here we have:
f(x) = 4*cos(x)
a = 7*pi
then, let's calculate each part:
f(a) = 4*cos(7*pi) = -4
df/dx = -4*sin(x)
(df/dx)(a) = -4*sin(7*pi) = 0
(d^2f)/(dx^2) = -4*cos(x)
(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4
Here we already can see two things:
the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.
so we only will work with the even powers of the series:
f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....
So we can write it as:
f(x) = ∑fₙ
Such that the n-th term can written as:
