6 of 15 to be laid off: find prob. given nurse is laid off

There are fifteen nurses who work the night shift in the Orthopedics ward of the local hospital. In an effort to save money, the hospital administrator decides to fire six nurses form that shift. You work at that hospital on that shift in that ward. Find the probability that you will be fired.

So to calculate probability- it is success/everything

The probability of you getting fired is 1- so the success is 1
Now to figure out everything I have no idea what to do- I need to find the number of ways that I can choose 6 nurses from the 15. First i thought it was 15 x 6=90, my professor told me that was wrong i thought it was 15 x 15 and 15 to the 6th power, each of them are wrong. I don't know how to calculate the denominator can anyone help me.

babyphattaluv23 said:

There are fifteen nurses who work the night shift in the Orthopedics ward of the local hospital. In an effort to save money, the hospital administrator decides to fire six nurses form that shift. You work at that hospital on that shift in that ward. Find the probability that you will be fired.

So to calculate probability- it is success/everything

The probability of you getting fired is 1- so the success is 1
Now to figure out everything I have no idea what to do- I need to find the number of ways that I can choose 6 nurses from the 15. First i thought it was 15 x 6=90, my professor told me that was wrong i thought it was 15 x 15 and 15 to the 6th power, each of them are wrong. I don't know how to calculate the denominator can anyone help me.

Click to expand...

Let's think of a different problem.

Suppose in a box, there are 9 blue pencils and 6 red pencils.

With your eyes closed, you pick up one pencil.

What is the probability that you picked up a red pencil?

What is the probability that you picked up a blue pencil?

the probability of getting a blue pencil is 9/15 and red is 6/15

but the answer cannot be 1/15- because I am trying to find out how many possible ways I can choose 6 nurses from the 15 without replacement

so another example would be
how many ways can you choose 6 names from a bag of 15 names without replacement? But I don't think I am doing it right

babyphattaluv23 said:

the probability of getting a blue pencil is 9/15 and red is 6/15

but the answer cannot be 1/15- because I am trying to find out how many possible ways I can choose 6 nurses from the 15 without replacement

so another example would be
how many ways can you choose 6 names from a bag of 15 names without replacement? But I don't think I am doing it right

Click to expand...

You are over thinking the problem:

Think of it this way:

If you picked a red pencil you are fired. <<< Probability 6/15

No that is wrong
the question is saying the probability of YOU getting - you are only one person I am sure of that so the numerator is 1
the denominator- how many possible ways can i choose 6 nurses from the 15 without replacement-that's what I do not know how to figure out

Think of it another way:

There is a box with 15 cards - 9 says "stay" and 6 says "fired"

You go pickup one card.......

Okay I understand what you're saying, but my professor told me that the numerator being 1 was correct he just wouldn't tell me the denominator its something i have to figure out

It's like this- Let's say there's 4 numbers in a bag right, 1,2,3,5- How many 2 digit numbers can be formed without replacement? Only 12

12, 13, 15
21, 23, 25
31, 32, 35
51, 52, 53

Those are the 12 digit numbers that can be formed without replacing the number I drew
If i were to replace the number the answer would be 16 because 4 x 4= 16 so i could have

11, 12, 13, 15
21, 22, 23, 25
31, 32, 33, 35
51, 52, 53, 55

That is the same thing with the denominator in the nurse problem, but 15 is a huge number and there are so many ways that I cannot write it out so I don't know how to get the answer