# Difference between revisions of "Eleisha's Segment 32: Contingency Tables: A First Look"

To Calculate

1. 20 our of 100 U.S. Senators are women, yet when the Senate formed an intramural baseball team of 9 people only 1 woman was chosen for the team. What is the probability of this occurring by chance? What is the p-value with which the null hypothesis "there is no discrimination against women Senators" can be rejected?

${\displaystyle {\text{P(Prob this occurs)}}={\frac {\text{Ways to choose one female and eight males}}{\text{Total ways to choose}}}={\frac {{20 \choose 1}{80 \choose 8}}{100 \choose 9}}\approx 0.30477}$

2. A large jelly bean jar has 20% red jelly beans, 30% blue, and 50% yellow. If 6 jelly beans are chosen at random, what is the chance of getting exactly 2 of each color? What is the name of this distribution?

This is a multinomial distribution.

${\displaystyle N=6,p_{r}=0.2,p_{b}=0.3,{\text{and }}p_{y}=0.5}$

Want to calculate, P, where P:

${\displaystyle P={\text{Prob}}({\text{2 red, 2 blue, 2 yellow}}|N,p_{r},p_{b},p_{y})={\frac {6!}{2!2!2!}}(0.2)^{2}(0.3)^{2}(0.5)^{2}=0.081}$

3. A small jelly bean jar has 2 red jelly beans, 3 blue, and 5 yellow. If 6 jelly beans are chosen at random, what is the chance of getting exactly 2 of each color? What is the name of this distribution?

This is a Hypergeometrical Distribution

Want to calculate:

${\displaystyle {\text{Prob(2 red, 2 blue, 2 yellow)}}={\frac {\text{Number of ways to get outcome}}{\text{Total ways of choosing}}}={\frac {{2 \choose 2}{3 \choose 2}{5 \choose 2}}{10 \choose 6}}\approx 0.1429}$