Exam 9: Counting, Probability Distributions, and Further Topics in Probability

Sketch a transition diagram for the given transition matrix. - $\left[\begin{array}{rrr}0.6 & 0.4 & 0 \\ 0.33 & 0.36 & 0.31 \\ 0 & 0 & 1\end{array}\right]$

Solve the problem. -An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.

Sketch a transition diagram for the given transition matrix. - $\left[\begin{array}{ll}0.3 & 0.7 \\ 0.6 & 0.4\end{array}\right]$

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. -One of each flavor

A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. -All cherry

Find the probability of the event. -A battery company has found that the defective rate of its batteries is .03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective.

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -More than one two

Solve the problem. -There are 12 students in a class: 9 are boys and 3 are girls. The teacher assigns seats at random. How many different boy/girl seating arrangements are possible?

Find the requested probability. -What is the probability that 14 rolls of a fair die will show three threes?

Solve the problem. -From 10 names on a ballot, 3 will be elected to a political party committee. In how many ways can the committee of 3 be formed if each person will have a different responsibility?