I need some step-by-step help for the following three basic problems.
1. a group of 8 professors and 5 administrators must select a team of 6 people from the group. They decide to select the team members randomly by drawing names from a hat. What is the probability that the selected team will consist of equal numbers of professors and administrators (3 of each)?
2. If you roll a single die 120 times, approximately how many times should you expect the number 5 to come up? Is the answer 1/6th of the time or 20 times?
3. In a certain craps game at a casino, if you place a bet on the "4", and a 4 comes up on a roll of the two dice before a 7 comes up, the payout odds are 9 to 5. Convert these odds to the player's win probability.
A jar contains 2 orange jellybeans, 6 red jellybeans, 6 green jellybeans and 4 yellow jellybeans. You pick a jellybean without looking.
a). What is the probability that it is orange?
b). What is the probability that it is orange, given it is NOT red?
c). What is the probability of picking yellow or green?
Complete, Neat and Step-by-step Solutions are provided in the attached file.