Since it's not mentioned I assume the Event of tossing a die twice are done simultaneously.
1- What is the theoretical probability that a coin toss results in two heads showing? I guess you mean: The theoretical probability of tossing 2 heads in 2 flips, if so P(1st Head) = 1/2 AND P(2nd Head) = 1/2, then the probability of getting 2 heads simultaneously is P(1st Head AND 2nd Head) = 1/2 x 1/2 = 1/4
2- What is the experimental probability that a coin toss results in two heads showing? In this case, I suggest that you toss a coin several times until 2 heads appear and then you calculate P: Assuming you get 2 heads (out of 10toss), the P(H) =2/10
3- What is the experimental probability that a coin toss results in two tails showing? Same logic as the previous one
4- What is the theoretical probability that a coin toss results in one head and one tail showing? If you get one Head, P(H) =1/2 and if you want a tail in the 2nd toss P(1/2). So P(one Head AND one tail) = 1/2 x 1/2 = 1/4
5- What is the experimental probability that a coin toss results in one head and one tail showing? Same as 3- or 4-
Data from random samples will not always include the same values. Values are chosen randomly and they may or may not be the same. So means will vary among samples.
