A coin will be tossed twice, and each toss will be recorded as heads ( H ) or tails ( T ). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the second toss is tails. Use the format  HT  to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas.

If a person draws a playing card and checks it’s suit and then spin a three-space spinner, describe the sample space of possible outcomes using C, D, H, S for the card outcomes abs 1, 2, 3 for the spinner outcomes.

A committee of 2 people is to be selected from 4 ​executives, Alam, Bartolini, Chinn, and Dickson. Write out the sample space​ S, choosing an S with equally likely​ outcomes, if possible. Then give the value of​ n(S) and tell whether the outcomes in S are equally likely.​ Finally, write the indicated events below in set notation. a. Dickson is on the committee. b. Bartolini and Dickson are not both on the committee. c. Both Bartolini and Chinn are on the committee.     What is the sample​ space? Use the first initial of each executive to write the events.     A. S=​{BA, BD, CA, CD, BC​}   B. S=​{AB, AC, AD, BC, BD, CD​} Your answer is correct.   C. S=​{AB, AC, BC​}   D. S=​{A, B, C, D​} The value of​ n(S) is 66. Are the outcomes equally​ likely?

A student flips a fair coin 6 times. Suppose now that after each flip the experimenter records the result (i.e. HH or TT) of the flip. Find the number of outcomes in this sample space

Multiple-choice questions each have five possible answers ( a, b, c, d )​, one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find ​P(CWC​), where C denotes a correct answer and W denotes a wrong answer. b. Beginning with CWC​ ,make a complete list of the different possible arrangements of two correct answers and one wrong answer ,then find the probability for each entry in the list. P(CWC​)= ​P(WCC​)= ​P(CCW)=   c. Based on the preceding​ results, what is the probability of getting exactly two correct answers when three guesses are​ made?