An experiment consists of tossing a fair coin (head H, and tail T) three times. The...
4 PROBABILITY (16) An experiment consists of tossing a fair coin (head and tail T) three times. The sample space S in this experiment is S - (HT), and a possible event Ecould be E = {H,H). (1) True. (2) False (17) Which of the following statements is true? (1) The set of all possible events of an experiment is called the sample space, S. (2) If an experiment is performed more than once, one and only one event can...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head, head, head”. Which of the following statements are true? a) The coin is not fair b) The coin’s tail probability is 1/6 c) The sequence "head, tail, head, head, head, head" is an outcome in the sample space. d) The sample space of the experiment is {head, tail}
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
Problem 7) True/False A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin. X follows a binomial distribution with n=20.p=0.5. Answer the following questions. True/False: In this problem, the random variable X is considered as a...
An experiment consists of first rolling a die and then tossing a coin: a. How many elements are there in the sample space? b. Let A be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal rounded to four decimal places.
7. A random experiment consists of tossing a coin 4 times. Describe the sample space of this experiment. In what proportion of all outcomes of the experiment will there be exactly 2 heads?
11. What are the possible combination outcomes when you toss a fair coin three times? (6.25 points) H = Head, T = Tail a {HHH, TTT) Ob. (HHH, TTT, HTH, THT) c. {HHH, TTT, HTH, THT, HHT, TTH, THH) d. (HHH, TTT, HTH, THT, HHT, TTH, THH, HTT} e. None of these 12. What is the probability of you getting three heads straight for tossing a fair coin three times? (6.25 points) a. 1/2 OD. 1/4 C. 118 d. 1/16...
If an experiment consists of tossing a coin, throwing a dice, and then selecting a vowel at random from all the alphabets, how many sample points are there in the sample space? What is the probability of obtaining a head, 6, and "e"?
3.1 An experiment consists of tossing a fair coin 5 times. (a) Find the probability mass and distribution functions for the number of heads realized. (b) Find the probability of realizing heads at least 3 times out of the 5 trials.
Consider the experiment of tossing a fair coin two times and the events: A={(H,H),(TH)), B=((H,H),(H,T), C={(TT)). The independent events are A) B and C only B) A and B only C) A and Conly D) Any two of them E) None of them Select one: A B С D E