Answer:
Step-by-step explanation:
Probability refers to chance of happening of some event.
Conditional probability is the probability of an event A, given that another event B has already occurred.
denote the two boxes.
In box 
:
No. of black balls = 1
No. of white balls = 1
In box 
:
No. of black balls = 2
No. of white balls = 1
Let B, W denote black and white marble.
So, probability that either of the boxes is chosen is 
Probability that a black ball is chosen from box =
Probability that a black ball is chosen from box 
To find:probability that the marble is black
Solution:
Probability that the marble is black = 
Answer and Explanation:
A function is said to be increasing, if the derivative of function is f’(x) > 0 on each point. A function is said to be decreasing if f”(x) < 0.
Let y = v (z) be differentiable on the interval (a, b). If two points z1 and z2 belongs to the interval (a, b) such that z1 < z2, then v (z1) ≤ v (z2), the function is increasing in this interval.
Similarly, the function y = v(z) is said to be decreasing, when it is differentiable on the interval (a , b).
Two points z1 and z2 Є (a, b) such that z1 > z2, then v (z1) ≥ v(z2). The function is decreasing on this interval.
The function y = v (z)
The derivative of function Y’ = v’(z) is positive, then the function is increasing.
The function y = v (z)
The derivative of function y’ is negative, then the function is decreasing.
Proofs are... well... just that. They are your proof for why a certain property works or what you did to show your work. So essentially, you just do math like normal, a proof is showing what you did and why it works.
