Statistics and Probability Answers

there are 250 residents in a community. they decided to set up a three person committee to advise them. the members are chosen at random. the first person chosen will become the chair. their racial/ethnic composition is as follows: 50% white. 30% black and 205 latino.
what is the probability of all three members being black? the chair is a white person? the chair is white or Latino?

Task
find the null hypothesis using chi-sqaure by having 69 as projected and 48 actual number of students, using 5% probability.

find the null hypothesis using chi-sqaure by having 69 as projected and 48 actual number of students, .05 level of significance.

6. The Senate consists of 100 senators, 2 from each of the 50 states. A Senate com- mittee of six is to be formed.
. (a) How many ways are there to form the committee from the 100 senators?
. (b) If at most one senator from each state can serve on the committee, how many ways are there to form the committee?

I have a pool of 3000 people. I need 5% of that pool randomly selected in the result set.
If I run my code, assigning a random number then pulling the Top 5%.

I seem to get some of the same people in the result set each time I run my code.

What is the probability or odds of this happening?

Thank you for any help you can offer.

Students must download monthly historical stock prices from two US stocks from
different industries for a period of 5 years. It is advisable to use excel spreadsheet
function.

Align the dates of the two stocks so that the returns of the two stocks are on the same
month and calculate the historical monthly returns of these stocks using the adjusted
closing prices from yahoo using monthly return =(Pricemonth2 – Pricemonth1) / Pricemonth1.
After which, find the average monthly return.

Using the monthly return, calculate the standard deviations using the function STDEV in
excel
Calculate the annualised expected returns (=12 x average monthly return) and standard
deviations of both stocks and the correlation of the returns using the function CORREL.
Students should comment on the risk and return for their two stocks of choice. Also
should comment on the correlation.

probability a family will have a female second child

If the correlation between two variables is .496, how much of the variance has not been accounted for

I put 32 chess pieces in a hat. I then proceeded to pull them out 2 at a time. If they are both black I put them in one pile. If they are both white, I put them in a second pile. If there is one of each color, I put them in a thrid pile. What is the probability that the number of pieces in the all black pile and the all white pile are equal?

In the statistical term, please define and explain with example the term " lack of realism"