Can you Please help answering this question for my Data Management. Thank you for helping.

#1) Discuss how you would design a probability experiment to determine the probability of rolling a 3 with a pair of dice. Briefly outline the steps you would follow to execute the experiment. Be sure to include the sample space, the number of trials, and a discussion on the differences between experimental and theoretical probability.

#2) Two fair dice are rolled. What is the probability of

A) rolling a 2, 4 times in a row?

B) rolling doubles or a number that is evenly divisible by 3?

#3) The probability that Jacqueline will be elected to the students' council is 0.6, and the probability that she will be selected to represent her school in a public-speaking contest is 0.75. The probability of Jacqueline achieving both of these goals is 0.5.

a)Are these two goals mutually exclusive? Explain your answer

b)Are these two goals independent? Explain your answer.

c) What is the probability that Jacqueline is either elected to the students' council or picked for the public-speaking contest?

#4) A bag contains 9 red marbles, 10 white, 5 blue. If 6 are drawn at random, what is the probability

a)3 blue

b)same number of each colour

c)NONE WILL BE RED

d)all 6 will be the same colour

#5) When Ayla improves her game of darts the chances that a she hits a bullseye is 0.65.

Assume that each throw is independent.

a)What are the chances that three darts fired in succession will all hit bullseye?

b)What is the probability that none will hit?

c)What is the probability that at least one will hit?

d)What is the probability that 2 will hit?