A financial analyst believes that if interest rates decrease in a given period, then the probability that the stock market will go up is $0\mathrm{.}80.$ The analyst further believes that interest rates have a $0\mathrm{.}40$ chance of decreasing during the period in question. Given the above information, what is the probability that the market will go up and interest rates will go down during the period in question.

$5.$ a$.$ Scholars and academic community have narrated the dichotomy between Confidence interval $($CI$)$ and Confidence Level $($CL$)$ with no truce, discuss.

b$.$ Mention and discuss the effect of the increase of sample size on margin of error