Question

A math teacher is randomly distributing 15 rulers with centimeter labels and 10 rulers without centimeter labels. What is the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels?

Answer 1

Let's call the event that she hands out a ruler with labels first A and
the event that she hands out a ruler without labels second B
We need
P(A) * P(B|A)
Where P(A) means "probability of A" and P(B|A) means "Probability of B given that A happened."

Answer 2

If we're looking at equally likely possibilities, probability is just
(number of "good" possibilities) / (total number of possibilities)
To calculate P(A), the "good" possibilities are the labeled rulers, which there are 15 of, and the total possibilities are 25 because there are 25 rulers total.
To get P(B|A), figure out the good and the total again, but assume she already handed out 1 marked ruler.

Answer 3

I'll let you try it.

Answer 4

no

Answer 5

Agree. That's wrong, fool.

Answer 6

Will A and B be independent events, mutually exclusive events, or non mutually exclusive events?

Answer 7

SmoothMath has the right technique

Answer 8

Crap, I mean \[ \frac {15}{25} \times \frac {10}{24} \]

Answer 9

that is better :)

Answer 10

I am becoming more fool everyday! :(

Answer 11

Not independent. If I hand out a marked ruler first, I have fewer marked rulers the second time, so I'm less likely to hand one out the second time. They are definitely dependent.
As for mutually exclusive, could both things happen? If they could, then they aren't mutually exclusive. Mutually exclusive would be like:
I'm flipping two coins. What's the probability that I flip 2 heads AND flip 1 tail?

Answer 12

This is standard,\[ (15C1 \times 14C1)/25 \times 24 \]

No idea what I thought before... :(

Answer 13

Ok, so i will have to use: P(A and B)/P(A) , right?

Answer 14

Think like this, you have 25 rulers, 10 of them are not labelled and 15 labelled.

Now, first you have to choose a labelled ruler our out 15, you can do that in 15 ways.

so the probability is 15/25

now you have to choose 1 ruler which is not marked from 10, we can do this in 10 ways.

but now we only have 24 rulers of both types,

so the probability is 10/24

Now, by our reasoning we have made these two as independent event, so the probablity of choosing a labelled and then unlabeled ruler is \[\frac{15\times 10}{25\times 24} \]

Answer 15

I appreciate all of you guys help. Thank you.