1) If a fair coin is tossed \(12\) consecutive times find the probability of tossing exactly \(9\) heads.
2) The pass rate on entry level actuarial exams is \(35\%\). If there is a group of \(50\) people taking the exams find the probability that exactly \(15\) of the people will pass the exams.
3) A survey shows that \(22\%\) of students bring their lunch to school. If you select \(10\) students randomly, what is the probability that at least one student in the group brings their lunch to school?
4) If you roll a fair six-sided die \(10\) consecutive times, what is the probability of getting a \(6\) at least twice?
5) Emmy makes \(68\%\) of the free throws she shoots. If she shoots \(50\) free throws, find the probability that she makes at least half of them. (Summation notation is your friend here)
For problems #6-10 construct a histogram and answer the following questions.
In a recent study it was found that more households have a Netflix subscription than a DVR. \(54\%\) of adults in the U.S. said they have a household Netflix subscription.
Suppose you select \(6\) adults randomly and survey them about if they have Netflix subscription.
Create a a binomial probability distribution for this situation.
6) What is the most likely outcome of your survey? Explain.
7) What is the probability that exactly \(1\) of the adults has a Netflix subscription?
8) What is the probability that at least one of the adults has a Netflix subscription?
9) What is the probability that none of the adults has a Netflix subscription?
10) Explain the relationship between the probability in #8 and #9.
Review
11) If there is a meeting of \(14\) people, how many different handshakes can take place?
12) Suppose you are lucky enough to find a savings account that pays out \(4\%\) annual interest. If the interest is compounded continuously how long will it take for your investment to double?
13) If \(\theta\) is an angle whose terminal side is in quadrant III and \(\cos \theta =- \large\frac{4}{5}\), find \(\cot \theta\).
14) Evaluate \(\large\frac{142!}{139!}\).
15) Find the inverse of \(f(x)=4 \ln (2x-3)\).
Solution Bank