# Prob. Solving

1. Sep 23, 2004

### Changoo

36 of 80 teachers at a local school are certified in CPR. In 180 days of school, assuming none of the teachers were ever absent, about how many days is it that the teacher on bus duty will likely be certified in CPR?

Can someone give some idea of how to solve this problem.

I notice that they want the probability that "the teacher on bus duty will likely be certified in CPR". So it is the probability of one teacher.

I did 180/36 =5 days. But I don't think that is write. I am currently learning discrete probability distributions.

I hope someone can help. Thanks

2. Sep 23, 2004

### vsage

Let me ask you something. How many times (on average) will a certain teacher have to do bus duty? What is the ratio of teachers who know CPR to teachers who don't? What's the probability that "certain teacher" in question knows CPR?

3. Sep 23, 2004

It's just a guess...

1 day: $$\left(\frac{36}{80}\right)$$

2 days in a row: $$\left(\frac{36}{80}\right)^2$$

3 days in a row: $$\left(\frac{36}{80}\right)^3$$

Then,

180 days in a row: $$\left(\frac{36}{80}\right)^{180}$$

Again, I'm not sure this is correct.

4. Sep 23, 2004

### HallsofIvy

What question is that supposed to be the answer to? The question originally asked said nothing about "days in a row".

5. Sep 23, 2004

### vsage

You're thinking more than you have to. Answer my original questions and I think the answer will jump out you.

6. Sep 23, 2004

That's why I said I wasn't sure. :rofl: Thanks for pointing it out.

$$\left(\frac{36}{80}\right)\cdot 180 = 81$$