4. Suppose you have two biased coins, but you don't know which coin is which. Coin 1 comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3. Suppose you pick a coin at random and flip it. Let C denote the event that coin i is picked . Let H and T denote the possible outcomes of the flip. (a) Draw a tree diagram for the experiment. (b) Given that the outcome of the flip is a head, what is P[CH], the probability that you picked the second coin? (c) Given that the outcome is a tail, what is the probability P[C|T] that you picked the

4. Suppose you have two biased coins, but you don't know which coin is which. Coin 1 comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3. Suppose you pick a coin at random and flip it. Let C denote the event that coin i is picked . Let H and T denote the possible outcomes of the flip. (a) Draw a tree diagram for the experiment. (b) Given that the outcome of the flip is a head, what is P[CH], the probability that you picked the second coin? (c) Given that the outcome is a tail, what is the probability P[C|T] that you picked the

Name: 4. Suppose you have two biased coins, but you don't know which coin i
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 4. Suppose you have two biased coins, but you don't know which coin is which. Coin 1comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3.Suppose you pick a coin at random and flip it. Let C, denote the event that coi

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Suppose we roll two six-sided dice. Consider event A as getting an odd number on die 1, event B asgetting an even sum for the two dice. Are event A and B independent?
2. A kindergarten class has 6 boys and 7 girls. At the end of each day, the teacher selects 5 students, uniformly at random, and asks them to help clean up the classroom. One of the boys in the class is named Vito. Show that, with probability = 38%, Vito and at least one girl will be amongst the 5 students asked to clean up today.
I need help solving this problem: Subjects for the next presidential election poll are contacted using telephone numbers in which the last 4 digits are randomly selected (with replacement). Find the probability that for one such phone number, the last 4 digits include at least one 0.
Consider two events A and B. The probability for event A is P(A) = 0.52. Suppose P(B|A) = 0.65 and P(B|AC) = 0.45. a. Find P(AC). b. Find P(An B). c. Find P(An B). d. Construct a probability tree diagram. See the diagram on pages 50 and 52 of the course packet. Find P(B). Find P(A/B). Are A and B mutually exclusive? Why or why not? Are A and B independent? Why or why not? U e. f. g. h.
2. A large population of crickets contains 30% who can chirp. Suppose 4 crickets are selected at random from this population, find the probability that (a) all can chirp, (b) at least one can chirp, and (c) exactly 2 can chirp.
Q4. Suppose you have a biased coin that has a probability of 0.6 of coming up heads. Toss this coin 20 times. a. Lets run this experiment 10 times and record the number of successes. Define heads as a success. (set.seed(0), this sets the seed for the random number generator so that you all get the same results.) b. Create the bar chart of successes. c. Repeat the experiment 100 times and solve for questions (a.) and (b.).
11. Consider the following experiment: Flip a coin. If heads, roll a die twice and record the sum of the outcomes. If tails, roll a die three times and record the sum of the outeomes. What is the probability the sum is 187
The chaper is Probability.
Consider the experiment: You ask someone two multiple-choice questions. Each question could be answered with Yes (Y), No (N), or Don't Know (D). (For example, if you ask someone these two questions, they could answer Yes to both of them, or Yes to the first one and Don't Know to the second one, etc.) Let A be the event that the person answers Yes to at least one question, and Let B be the event that the person answers No to the second question. How many elements are in the sample space? What elements are in A ∩ B? What elements are in A ′?
7. The table below gives the probabilities of a few dependent events. The probability of an arrow hitting the target is 0.87. The probability of an arrow hitting the target and landing in the inner circle is 0.82. The probability of rain during the football game is 0.68. The probability of Rodrick's college team winning the football game when it rains is 0.45. The probability of Maria serving to the forehand in the first serve of a tennis match is 0.66. The probability of serving to a backhand in her second serve and to the forehand in her first serve is 0.48. The probability that while bowling Ralph gets a strike in the first game is 0.32. The probability that he gets a spare in the second game and a strike in the first game is 0.30. Which of the following statements has the greatest probability? A. the probability of getting a spare in the second game given that Ralph got a strike in his first game O B. the probability of serving to a backhand in the second serve given that Maria…
Two students agree to meet at the Science Library between 7pm to 8pm next evening.They also agree that the student arriving first will wait until this student waits for half an hour.What is the probability that they will meet if they arrive at the Science Library between 7pm to8pm next evening randomly?
-AWCO by a 2. A pair of dice is rolled thrice. What is the probability of getting doubles in the three rolls? 3. There are 7 green, 4 blue and 9 red marbles in a box. A marble is drawn at random and after recording its color, the marble is returned in the box. Another marble is then drawn. What is the probability that both marbles are red? 4. Suppose a football player has a 65% chance of making a goal that he can keep each time he tries to make a goal. What is the probability that he makes a goal the first three times he tries to but not on the fourth try?