Question 1
Eight balls numbered from 1 to 8 are placed in an urn. One ball is selected at random. Find the probability that it is NOT number 2.

87.5% probability that it is NOT number 2.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Any ball not numbered 2. So 1,3,4,5,6,7,8. So 7 desired outcomes, which means that

Total outcomes:

All balls, which are 8. So

Probability:

87.5% probability that it is NOT number 2.

probability for j is 1/4

while

a is 1/6

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.