3. In this question we simulate the rolling of a die. To do this we use...
3. In this question we simulate the rolling of a die. To do this we use the func- tion runif (1),which returns a randomnumber in the range (0,1). To get a random integer in the range (1,2,3,4,5,6), we use ceiling(6 runif (1)) or if you prefer, sarple(1:6,size-1) will do the same job. (a). Suppose that you are playing the gambling game of the Chevalier de Méré. That is, you are betting that you get at least one six in 4...
Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and observe a 3 on 90 of the 500 rolls. You estimate the probability of rolling a 3 to be 0.18 Choose) You roll a fair six-sided die 10 times and observe a 3 on all 10 rolls. You bet the probability of rolling a 3 on the next rollis close to O since you have already had 10 3's in a row You assign...
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
Write a C PROGRAM that will simulate rolling a die. When rolling a die, one will get a die face value of 1-6. We can use rand function and math ceiling function to get a random number of 1-6 generated. The program will simulating rolling 5 dice simultaneously and store their face values into an array of size 5. The program will keep rolling the dice and print the following: 1. All face values in one line 2. If any...
Use the "at least once rule to find the probability of getting at least one 4 in six rolls of a single fair die. The probability is _______
Suppose you physically simulate the random process of rolling a single die. (a) After 10 rolls of the die, you observe a "one" 2 times. What proportion of the rolls resulted in a "one"? (b) After 20 rolls of the die, you observe a "one" 6 times. What proportion of the rolls resulted in a "one"? (a) The proportion was Simplify your answer. Do not round.)
15. Your friend challenges you to a game. She says that she is going to roll 2 6-sided dice. If the first die rolls at least 5, you win if the second die rolls less than 5. If the first die rolls less than 5, you win if the second die rolls at least 5. This seems fair. Is it? (a) What is the probability that you win this game? To incentivize you, your friend says that she will pay...
Topic: Probability Suppose you physically simulate the random process of rolling a single die. (a) After 10 rolls of the die, you observe a "one" 1 times. What proportion of the rolls resulted in a "one"? (b) After 20 rolls of the die, you observe a "one" 3 times. What proportion of the rolls resulted in a "one"? (a) The proportion was _________. (b) The proportion was __________. (Simplify your answer. Do not round.) Note: I saw the solution posted...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
Sally is rolling a fair 6-sided die. What is the probability that it takes 4 rolls for her to get a six? 0.5787 0.005 0.5177 0.096 0.1667