You flip a coin four times and observe whether a head or a tail occurs on each flip. How many outcomes are in the sample space for this random phenomenon?
Since for each flip, two outcomes are possible,
Number of outcomes in the sample space = 2*2*2*2 = 16
You flip a coin four times and observe whether a head or a tail occurs on...
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}
Flip a coin twice and observe its face side. Assume that the coin is unfair with P(head)=0.6. Define the following events: •A: you get at least one head •B: you get at least one tail Write out sample space S, events A,B by listing all possible outcomes. (b) FindP(A), P(B) (c) FindP(A∪B),P(A∩B) (d) FindP(A|B) (e) Are A,B independent? and why?
Suppose we flip a coin three times, thereby forming a sequence of heads and tails. Form a random vector by mapping each outcome in the sequence to 0 if a head occurs or to 1 if a tail occurs. (a) How many realizations of the vector may be generated? List them. (b) Are the realizations independent of one another?
Problem 4: You flip a fair coin three times. Each time you get a head, you win S2. Each time you get a tail, you lose $1. What is your expected winning from this game?
Roll 6-sided dice. If “1, 2 or 3” occurs in the first roll, flip a coin. If “4, 5 or 6” occurs, roll 6-sided dice again. What is the sample space of this experiment, Show with the tree diagram technique. How many sample points are in the sample space? What is the probability that flips results in a head?
Problem 2. a. You flip a coin and roll a die. Describe the sample space of this experi ment b. Each of the 10 people flips a coin and rolls a die. Describe the sample space of this c. In the erperiment of part b. how many outcomes are in the event where nobody rolled d. Find the probability of the events in part c. What assumptions have you made? experiment. How many elements are in the sample space? a...
An experiment consists of tossing a fair coin (head H, and tail T) three times. The sample space S in this experiment is S = {H, T}, and a possible event E could be E = {H,H}. (1) True. (2) False.
A coin will be tossed multiple times. Probability of head is 1/2, and probability of tail is 1/2. they are independent from each other. X is a random variable that counts how often the coin must be tossed until the first head appears. calculate for all k=1,2,3,..., how big the probability is for: i) X=k ii) X>k iii) X<k
A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3. Denote the outcome to be 1 if you get a head and 0 if a tail. (i) Write down the sample space Ω. (ii) What is the probability of the event that you get a head or a tail at least once? (iii) If you get eight same toss's you will get x dollars, otherwise you will lose 1 dollar. On average, how large...