Probability help! I am teaching a class of 100 students that has 35 men and 65 women.
a.What proportion of the class are men?  What proportion of the class are women?  Show two different ways to calculate the proportion of seniors.
b.I randomly choose 10 students (with replacement) from the class.  Calculate the probability that 8 of those students are women.  List the equation, define the variables, and calculate the answer. 
 A: For question (a), i can just say that the second way of calculion is 1 minus the proportion of the other.
(b), the question can be solved using binomial distribution, the probability of choosing a woman is p, so the prob of man is 1-p, then we get the prob is, 
$$\binom{10}{8}p^8(1-p)^2$$
A: What I would think about seniors, there are generally two ways of calculating them 
either directly, $ \frac{\#\{ \text{seniors}\} }{ \#\{ \text{Students}\}} $, or a second way using proportion of male and females in class 
$$ \frac{\#\{ \text{seniors}\} }{ \#\{ \text{Students}\}} =  \frac{\#\{ \text{male seniors}\} + \# \{ \text{female seniors}\} }{ \#\{ \text{Students}\}} = 
\\ \frac{\# \{\text{male} \}\times  \# \{ \text{male seniors}\}  }{ \# \{\text{male} \} \times \#\{ \text{Students}\}} +\frac{\# \{\text{female} \} \times  \# \{ \text{female seniors}\}  }{ \# \{\text{female} \} \times \#\{ \text{Students}\}}  = \\  \text{proportion of males }\times \frac{ \# \{ \text{male seniors}\}  }{ \# \{\text{male} \}} + \text{proportion of females} \times \frac{ \# \{ \text{female seniors}\}  }{ \# \{\text{female} \}} = \\ \text{proportion of males in calss}\times \text{proportion of senior males within males} + \text{proportion of females in calss}\times \text{proportion of senior females within females}  $$
Well, I guess this is a very detailed breakdown. Now for part b) Dylan Zhu has the correct interpretation.
