1) Use the counting techniques from the last chapter. A bag contains two red mar

Question

1) Use the counting techniques from the last chapter. A bag contains two red marbles, two green ones, one fluorescent pink one, two yellow ones, and two orange ones. Suzan grabs four at random. Find the probability of the indicated event.

She gets one of each color other than fluorescent pink, given that she gets the fluorescent pink one.

2) Say whether the given pair of events is independent, mutually exclusive, or neither.

A: Your first coin flip results in tails.
B: Your second coin flip results in heads.

a) independentmutually

b) exclusive

c) neither

3) A market survey shows that 50% of the population used Brand Z computers last year, 10% of the population quit their jobs last year, and 5% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting your job independent?

Yes or No    

4) Is a user of Brand Z computers more or less likely to quit a job than a randomly chosen person?

a) A user of Brand Z computers is as likely to quit a job as a randomly chosen person.

b) A user of Brand Z computers is less likely to quit a job than a randomly chosen person.   

c) A user of Brand Z computers is more likely to quit a job than a randomly chosen person.

5) The table shows the results of a survey of 100 authors by a publishing company.

Compute the following conditional probability.

An author is established, given that she is successful.

New Authors Established Authors Total Successful 10 25 35 Unsuccessful 15 50 65 Total 25 75 100

Explanation / Answer

1. Let say P(A)=probability that she gets one of each color other than fluorescent pink

and P(B)=probability that she gets the fluorescent pink one.

so we have to find P(A|B)

according to Bayes theorem P(A|B)=P(B|A)*P(A)/P(B)

Now P(B|A) is probablity rhat she gets the fluorescent pink one given that she gets one of each color other than fluorescent pink which is not possible so P(B|A)=0

so P(A|B)=0

2. a. two events are mutually independent if P(A)=P(A|B)

now lets say the occuring of first event has a probability of P(A) and second have P(B)

then P(A)=0.5 P(A|B)=(0.5*0.5)/0.5=0.5 so P(A)=P(A|B)

so they are mutually independent

3. yes P(A)= probability that population used Brand Z computers last year=0.5

P(B)= probability that the population quit their jobs last year=0.1

so P(A|B)=.05/0.1=0.5

so P(A)=P(A|B)

so they are mutually independent

4. a) because both events are mutually independent

5. no of author which are successful=35 and no of author which are successful and establised are=25

so conditional probability=25/35=5/7=0.714

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