Consider an experiment: tossing a coin three times, and observe head/tail facing up for each time....

Consider an experiment: tossing a coin three times, and observe head/tail facing up for each time.

a) What is the sample space?

b) List sample points in the event A that there are more tails than heads.

c) List sample points in the event B that exact 2 tails face up.

d) find the probabilities: P[A], P[B], P[A∩ B], P[AU B].

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

1. A coin is tossed 100 times, each resulting in a tail (T) or a head...

1. 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?

1. List the simple events of tossing a coin three times that includes one head. 2....

1. List the simple events of tossing a coin three times that includes one head. 2. In rolling a die once, A is the event of getting odd numbers outcome. Then define the complement of A. 3. Given P(A) = 0.7, find P(Ā). 4.In rolling a die once, A is the event of getting even numbers and B is the event of getting number 5. Then P(A or B) = 5. In rolling a die twice, A is the event...

A player tosses a fair coin n times. Each time, if the coin lands on Head,...

A player tosses a fair coin n times. Each time, if the coin lands on Head, the player win a dollar, otherwise, the player loses a dollar. What is the expected earning of the player? What is the variance of the earning of the player? Now the player apply a new strategy: the player will play the game until he gets a head. What is the expected earning of the new strategy? Does the result depend on n?

Peter and John are tossing a coin. If it is a Head, then peter will give...

Peter and John are tossing a coin. If it is a Head, then peter will give John 1dollar. If it is a Tail, then John will give Peter 1dollar. Suppose Peter has a dollar, John has b dollar. Question: the probability that Peter wins all the money from John.

Flip a coin 10 times. Put a 1 each time the coin comes up heads and...

Flip a coin 10 times. Put a 1 each time the coin comes up heads and a 0 each time the coin comes up tails. Count the number of heads you obtained and divide by 10. What number did you get? a. Is the number you obtained in part (a) a parameter or a statistic? b. Now flip the coin 25 times. Put a 1 each time you obtain a heads and a 0 for tails. Count the number of...

Write an application that simulates coin tossing. Let the program toss a coin each time the...

Write an application that simulates coin tossing. Let the program toss a coin each time the user chooses the “Toss Coin” menu option. Count the number times each side of the coin appears. Display the results. The program should call a method flip( ) that takes no arguments and returns a zero to represent a tail or a one to represent a head. There is a Random class that will allow you to generate a random integer. Import it from...

Problem 1 [20 pts]: An experiment consists of tossing a coin 6 times. Let X be...

Problem 1 [20 pts]: An experiment consists of tossing a coin 6 times. Let X be the random variable that is the number of heads in the outcome. Find the mean and variance of X. Thank You

A fair coin will be tossed three times. (a) Indicating a head by H and a...

A fair coin will be tossed three times. (a) Indicating a head by H and a tail by T write down the outcome space. (b) What is the probability that on the first toss the outcome with a tail? (c) What is the probability of obtaining exactly two heads from the three coin tosses? (d) What is the probability that the first toss gives a tail and exactly two heads are obtained from the three coin tosses? Are the outcomes...

Suppose we are flipping a coin with Head (H) and Tail (T) sides. The coin is...

Suppose we are flipping a coin with Head (H) and Tail (T) sides. The coin is not balancedwith 0.6 probability of H coming up (and 0.4 of T). Compute the probabilities of getting: a)HTHT b)THTTE c)Exactly 1 Head out of a sequence of 4 coin flips. d)Exactly 1 Tail out of sequence of 4 coin flips

An experiment is to flip a coin until a head appears for the first time. Assume...

An experiment is to flip a coin until a head appears for the first time. Assume the coin may be biased, i.e., assume that the probability the coin turns up heads on a flip is a constant p (0 < p < 1). Let X be the random variable that counts the number of flips needed to see the first head. (a) Let k ≥ 1 be an integer. Compute the probability mass function (pmf) p(k) = P(X = k)....

Subjects