Jurors. From 10 men and 8 women in a pool of potential jurors, 12 are chosen at random to constitute a jury. Suppose that you observe the number of men who are chosen for the jury. Let A be the event that at least half of the 12 jurors are men, and let B be the event that at least half of the 8 women are on the jury. a. Determine the sample space for this experiment. b. Find (A or B), (A&B), and ( A&(notB)), listing all the outcomes for each of those three events. c. Are events A and B mutually exclusive? Are events A and (not B)? Are events (not A) and (not B)? Explain.

Question 1Suppose we have an experiment that consists of flipping a coin 5 times.i. Find the total number for the outcomes for this experiment? ii. List all the elements in the sample space?iii. Find the probability that tails will be occurring at least 2 times on three coin flips?iv. Find the probability of getting all Head and all Tail on five coin flips?Question 2A bag has 10 blue balls and 5 red balls. 2 balls are to be drawn successively and without replacement. What is the probability that the first ball is red and the second is blue?Question 3Two coins are loaded so that each comes up heads 80% of the time when tossed. If the coins are both tossed simultaneously, i. What probability will the result be both are Tail?ii. What probability will the result give Head and Tail?

A sports arena has three entrances (E1, E2, E3) and four different exits (X1, X2, X3, X4). As spectators come in, they enter through a random entrance E1,E2, or E3 and then exit through a random exit (X1,X2, X3, or X4). a. Create the sample space for this experiment listing all possible entrances and exits a spectator may use. Hint, how many outcomes are there? b. What is the probability a spectator enters from E3 and exits from X4? c. What is the probability a spectator does not enter from E1?

Suppose our experiments consist ofrolling a six-sided die. Then we can define the appropriate sample space as S ={1,2,3,4,5,6}.I.What is probability that we roll a 2?II.What is probability that we roll a 2 or 5?III.What is probability that we roll an even number?