Business Essay

Question 1:

Sample space: a list of all possible outcomes of the random experiment

Event: a collection or set of one or more simple events in a sample space

Probability of an event: the sum of the probabilities of the simple events

Random experiment: an action or process that leads to one of several possible outcomes

The first step in the process of assigning probabilities is to produce a list of the outcomes. The list of outcomes must be exhaustive, which means all possible outcomes must be included. Additionally, the outcomes must be mutually exclusive, which means no two outcomes can occur at the same time.

Question 2:

Consider the following events:

O= The students does not have a credit card in their own name

C= The student has at least one credit card in their own name

F= The student has at least one credit card in her own name and pays her credit card balance in full each month

B= The student has at least one credit card in her own name and maintains a credit balance

FAN NOTES: in this scenario, O+C=S, C=B+F, or O+B+F=S

The events C and B are not mutually exclusive.

The events O and F are not exhaustive.

The events O and C are mutually exclusive.

The events B and F are exhaustive.

Event B is a simple event.

        A simple event is an individual outcome of a sample space. For this particular experiment, outcomes O, F, and B are simple events.

The set S={O,C,B} is not the correct description of the sample space for the random experiment because the events in S are not mutually exclusive.

P(F)=0.21

P(C)=0.29

P(B)=0.08

Question 3: Scenario: rock-paper-sissor game

The probabilities are assigned using the subjective approach.

Suppose that flat mate B’s probability assignments are correct. What can you say about P(SA), and probability that flat mate A choose scissors?

        P(SA)=0.06

        0<=P(SA)<=1

Assume that flat mate B’s probability assignments are correct. Flat mate B would like to use the hand signal with the highest probability of winning the game. What would you advise flat mate B to use? (Paper)

If flat mate go paper, and flat mate B took the advice to choose the highest probability of winning, then flat mate B tied the game.

Question 4:

Assume both flat martes’ choices of rock, paper and scissors are random, independent and equally likely. Define event A as the event that flat mate A wins the game and gets to sit in the front seat.

Event A is composed of the following simple events: A={RA,SB;PA,RB;SA,PB}

What is the probability of event A? (0.33)

Let event C be the event the game ends in a tie. Event CV is composed of the following simple events: C={RA,RB;PA,PB;SA,SB}

What is the probability of event C? (0.33)

These probability approach is classical approach.