Probability question help

finitehelp · 2012-03-01 12:19:37

i am at a loss. Please Help

1.Many companies test prospective employees for drug use. Suppose a company uses a test that is 98% accurate that is it correctly identifies an applicant as a user or nonuser with probability .98. The test is performed on each applicant twice and the outcomes are independent.
a) Use a tree diagram to sketch this two stage experiment.

b) Find the probability that a nonuser fails both tests.

c) Find the probability that a user fails at least one test.

d) Find the probability that a user passes both tests.

2. Two representatives are randomly selected from a list of six people, 4 male, 2 females. Let the random variable X represent the number of females selected.

a) Construct a probability distribution table for the random variable X.

b) What is the probability that there will be at least one female representative?

c) What is the probability that there will at most one female representative?

d) Calculate the mean and standard deviation for the random variable X.

MathsIsFun · 2012-03-01 13:12:38

Start here: Probability Tree Diagrams

finitehelp · 2012-03-02 02:20:58

I believe for the first question

b. .004
c. .9996
d. .004

But I am having trouble with that tree diagram still. I drew one on the test and got it completely wrong

finitehelp · 2012-03-02 03:38:51

Can anyone help this is one of the problem from my final I failed. The retest is in two day and i want to understand. please help

Bob · 2012-03-02 04:28:28

hi finitehelp

I'm not getting any of those answers, sorry.

See below for the tree diagram and the calculations you need to do to get these correct.

The test is either correct or incorrect so it is irrelevant whether the person is a user or not; just did the test get it right?

Please complete these and post back your answers. Then we'll have a look at the next part.

Bob

finitehelp · 2012-03-02 04:30:52

MathsIsFun wrote:

Start here: Probability Tree Diagrams

I though the answer was

Pass-------Pass or fail
/

\
Fail-------Pass or fail
My professor said it was wrong. Where did i go wrong

Bob · 2012-03-02 04:33:13

hi

great that we are both on line at the same time.

stay on line and we can work it through now.

look at post 5.

Bob

finitehelp · 2012-03-02 04:37:11

b. .0004

c. .50

d. .0004

Heres what i think

Bob · 2012-03-02 04:41:25

b is correct.

Let's get d next as it's easier to then get c.

For d you should be doing 0.98 x 0.98

Bob

finitehelp · 2012-03-02 04:42:43

c. i think is .0396 sorry

finitehelp · 2012-03-02 04:45:24

so d is .9604 because they pass both here right

Bob · 2012-03-02 04:50:57

hi finitehelp,

Now all your answers are right. Well done!

I'm just making the distribution table for you.

it's easy for me to show it on paper but it takes a little longer to make it in a form I can post so please be patient.

Bob

finitehelp · 2012-03-02 04:51:58

I will thank you so much. it feels so good to understand

Bob · 2012-03-02 04:59:03

OK, here we go.

You are picking two people.

If you want both males you have 4 chances out of 6 for the first one and 3 chances out of 5 for the next.

So that gives

At this stage I advise you not to cancel these down. We'll do that at the end.

Look at the table and if it makes sense try to complete the P(X) column.

Post your results. No need to try and make a table, just post the fractions out of 30.

Bob

Bob · 2012-03-02 05:00:14

Whoops! Just edited that post as it had a typo!

I meant P(both male)

I see you are off line so I'm off to do something else for a while.

I'll check back in 45 mins.

Bob

finitehelp · 2012-03-02 05:38:37

well from the diagram i think b and c is 8/15

Bob · 2012-03-02 05:52:52

They are not both 8/15.

you have rushed ahead a bit beyond what I was planning. i want you to understand this well enough, so that you can do these in an exam.

Let's back track a bit.

In the table I partly did the first P(X) = 4/6 x 3/5

So what does that come to? Give an asnwer like this ???/30

Then do the other two rows.

Then we'll see how you can test for yourself that you've done the table correctly.

then we'll answer all the questions.

Bob

ps. I see you've got another post on the go. I recommend you sort these out one at a time.

finitehelp · 2012-03-02 05:56:07

ok so that is 2/5 right?

finitehelp · 2012-03-02 05:59:22

I will wait until i finish this one before the next one. I am looking to understand it more than anything
I would link if i just multiply 4/6 x 3/5
That would be the answer

Bob · 2012-03-02 06:01:14

Much too fast. One of your answers was correct but the other wasn't so I'm trying to check if that correct one was just luck.

here's the table again. What have you got for the three fractions in the three rows?

Bob

finitehelp · 2012-03-02 06:04:42

row 1 2/5

row 2 8/15

row 3 1/15

Bob · 2012-03-02 06:10:28

OK. All correct.

But I suggest you leave these not cancelled.

So

12/30
16/30
2/30

Why?

because now it is easy to test if they add up to 30/30.

12 + 16 + 2 = 30 so you can see that you are doing this right.

Now for the questions.

P(at least one female) means P(exactly one female) + P(exactly two females).

So what do you get for that?

Bob

finitehelp · 2012-03-02 06:11:49

18/30

Bob · 2012-03-02 06:14:19

Correct.

Now for P(at most one female) this means P(exactly one female) + P(no females)

What do you get for that?

Bob

finitehelp · 2012-03-02 06:15:26

28/30

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#1 2012-03-01 12:19:37

Probability question help

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