Answer:
The probability this could occur by chance is approximately 0.003053.
Step-by-step explanation:
This problem can be solved with a binomial distribution, if we imagine that by the end of January the stock market will follow the same pattern for the rest of the year we can define the following random variable:
"The stock market will be up for the rest of the year",
and 
if by the end of January the stock market is up and 
otherwise, this way 
, where p is the probability of success. Next we can define the following random variable:
"Sum of all years where the stock market was up"
Now, the sum of a Bernoulli random variables is a Binomial random variable, in other words 
, where n is the number of trials and p is the probability of success. The pdf of Y is given by:
The question give us the 
, 
and 
. Now we just have to solve it:
Which is highly unlikely to happen.
Answer:
$63.60
Step-by-step explanation:
After the 25% markup, the price is ...
$60 + 0.25·60 = $75
After the 20% discount, the price (before tax) is ...
$75 - 0.20·75 = $60
After tax is added, the price is ...
$60 + 0.06·60 = $63.60
_____
Effectively, the original price is multiplied by ...
(1.25)·(0.80)·(1.06) = 1.06
The resulting price with tax is ...
1.06·$60 = $63.60
It's a quadratic equation. Solve it through factorisation.
5s^2 - 14s - 3 = 0
(5s + 1)(s - 3) = 0
5s + 1 = 0
or
s - 3 = 0
Therefore
s = -1/5
or
s = 3
