# Math Help - Probability question...easy?

1. ## Probability question...easy?

the answer to this is probably totally obvious but i suck at probablility

A 5th grade class has sixteen girls and twelve boys. Each week, the teacher randomly draws a student to clean out the fish tank. Once a student is chosen, they are not put back into the drawing until everyone else has had a turn. What is the probability that:
a. A boy will be chosen the first week and a girl the second week.
b. Sarah (a girl) will be the last student chosen if the order of the students before her does not matter

can someone help me with this in a way i can understand?

2. Originally Posted by xitsxhuffx
the answer to this is probably totally obvious but i suck at probablility

A 5th grade class has sixteen girls and twelve boys. Each week, the teacher randomly draws a student to clean out the fish tank. Once a student is chosen, they are not put back into the drawing until everyone else has had a turn. What is the probability that:
a. A boy will be chosen the first week and a girl the second week.
b. Sarah (a girl) will be the last student chosen if the order of the students before her does not matter

can someone help me with this in a way i can understand?

for part a lets look at it this way.

the class has 16 girls and 12 boys 28 total people.

so the pobability of picking a boy the first week is

$\frac{ \overbrace{ \binom{12}{1}}^{pick1boy} \cdot \overbrace{\binom{16}{0}}^{pick0girls}}{\underbrac e{\binom{28}{1}}_{pick 1 Student from 28}}=\frac{12}{28}=\frac{3}{7}$

Now we have reduced the sample space( there is one less boy)
16 girls 11 boys 27 total students
Now we want to pick a girl so

$\frac{ \overbrace{ \binom{11}{0}}^{pick0boys} \cdot \overbrace{\binom{16}{1}}^{pick1girl}}{\underbrace {\binom{27}{1}}_{pick 1 Student from 28}}=\frac{16}{27}=\frac{16}{27}$

Since we want both events to happen we multiply them together and get

$\frac{3}{7} \cdot \frac{16}{27}=\frac{1}{7} \cdot \frac{16}{9}=\frac{16}{63}$

Think about part b and post what you come up with

Good luck.

3. Originally Posted by xitsxhuffx
A 5th grade class has sixteen girls and twelve boys. Each week, the teacher randomly draws a student to clean out the fish tank. Once a student is chosen, they are not put back into the drawing until everyone else has had a turn. What is the probability that:
a. A boy will be chosen the first week and a girl the second week.
b. Sarah (a girl) will be the last student chosen if the order of the students before her does not matter
The probability that a male is chosen first is $\frac {12} {28}$. Do you see why?
Given that a male is chosen first, then the probability that a female is chosen second is $\frac {16} {27}$. Do you see why?
So what is the answer to part (a)?

For part (b), the total number we an arrange the class is $28!$.
In $27!$ of those ways Sara is at the end of the arrangements.
So what is that ratio?

4. Part a isnt the part i am having trouble with...its part B that isnt making sense to me.

isnt the chance just 1 out of 28? she has just as much chance as every other student to be last. thats the only answer i can come up with. help please?