A. If an experiment can be described as a sequence of 4 steps with 2 possible ou

Question

A. If an experiment can be described as a sequence of 4 steps with 2 possible outcomes on the first step, 2 possible outcomes on the second step, 3 possible outcomes on the third step, and 3 possible outcomes on the fourth step, what is the total number of experimental outcomes (branches in the tree diagram)? Enter your response as an integer (i.e. 25).

B. Assume a medical clinic wants to determine the number of unique Saturday schedules. If the number of doctors on staff is 8 and the number in a Saturday schedule is 5, what is the number of unique schedules (at least one doctor is different)? Enter your response as an integer (i.e. 25). Use Excel's combin function.

C. Assume a medical clinic wants to determine the number of all schedules where the doctors on-call are in an ordered list showing the first to be called at the top and the other(s) below. There are 7 doctors that could be on the list and the number on the list is 4, how many unique on-call lists could be created? Enter your response as an integer (i.e. 25). Use Excel's permut function.

D. A bank has the following data on the gender and marital status for a sample of customers.

What is the probability that a randomly chosen customer is Single or Female (this is a union probability)? Enter your response as a decimal to two decimals (i.e. 0.12).

E. If the probability of an event (A) is 0.11 and the probability of a second event (B) is 0.5, what is the probability of events A or B occuring, assuming they are mutually exclusive events? Enter your response to two decimals (i.e. 0.12)

F. If the probability of an event is 0.78, the probability of its complement is? Enter your response to two decimals (i.e. 0.12)

G.A bank has the following data on the gender and marital status for a sample of customers.

What is the probability that a randomly chosen Female customer is Single (this is a conditional probability)? Enter your response as a decimal to two decimals (i.e. 0.12).

H. A bank has the following data on the gender and marital status for a sample of customers.

What is the probability that a randomly chosen customer is Single and Female (this is a joint probability)? Enter your response as a decimal to two decimals (i.e. 0.12).

I. A bank has the following data on the gender and marital status for a sample of customers.

What is the probability that a randomly chosen customer is Single (this is a marginal probability)? Enter your response to two decimals (i.e. 0.12).

J. If the probability of an event (A) is 0.17 and the probability of a second event (B) is 0.41, what is the probability of events A and B occuring, assuming they are independent events? Enter your response to two decimals (i.e. 0.12)

K. Of the last 158 customers entering a shop, 26 have made a purchase. If the relative freqency method for computing probability is used, the probability that the next customer will make a purchase is? Enter your response to two decimals (i.e. 0.12)

L. Assume the prior probability of an event "A1" occuring is P(A1)=0.52, the conditional probability of "B" given that "A1" has occured is P(B|A1)=0.76, the conditional probability "B" given that "A1" has not occured is P(B|not A1)=0.23, what is the posterior probability of event "A1" occurring if "B" has occurred "P(A1|B)"? Enter your response as a probability, to two decimals (i.e. 0.12). Use the tabular approach for Bayes' Theorem shown in the book.

Explanation / Answer

a)

Their are 4 steps , with 2 posiible outcome at step 1 and step 2 and 3 possible outcome at step 3 and step 4.

So total outcome= 2*2*3*3

So total outcome are 36.

Using the number of comination as [ 8 5] by excel function of combine

COMBIN(8,5)= 56

we can calculate it therotically also,

Outcome= 8!/(8-5)!*5!=56

The number of unique schedule is 56.

Total doctors(n)=7

Assign numbers(k)=4

Outcome= PERMUT(7,4)                                         excel function

Outcome=840

Can be done by therotically as 7!/(7-4)!=840

840 unique on-call list can be created.

        P(F)= probability of female

        P(S)= probability of single

       P(SN)= probability of married

P(S intersection M)=39

P(S intersection F)=31

P(SN intersection M)=66

P(SN intersection F)=75

P(F)= P(S intersection F)+P(SN intersection F)=31+75=106

P(F)=106

P(S)=P(S intersection M)+P(S intersection F)=39+31=70

P(S U F)= P(S)+P(F)-P(S intersection F)

              = 70+106-31

P(S U F)=145

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