A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots), Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment Compute the probability of each of the following events Event A: The sum is greater than 9. Event B: The sum is an even number.
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 7. Event B: The sum is divisible by 6.
An ordinary( fair) die is a cube with the numbers 1 through 6 on the sides ) represented by painted spots). Imagine that such die is rolled twice in succession and that the face values of the two rolls are added together. this sum is recorded as the outcome of a single trial of a random experiment What is the probabilty of each of the following events of, event A( the sum is greater than 6) and event B(the sum...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Suppose that we roll a fair die that has two faces numbered 1, two faces numbered 2, and two faces numbered 3. Then we toss a fair coin the number of times indicated by the number on the die and count the number of heads. How much information is obtained (on the average) by this procedure?
You have two fair, 6-sided dice. Die 1 has 4 white faces and 2 black faces. Die 2 has 2 white faces and 4 black faces. You roll Die 1. If it comes up white, then Die 1 is the “chosen die” and you put Die 2 away, but if it comes up black, then Die 2 is the “chosen die” and you put Die 1 away. You now roll the chosen die twice, noting the color that comes up...
7. Is the die fair? You suspect that a die has been changed so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You to the die 600 times and obtain the following result. Outcome Count 1 2 3 4 87 80 125 117 5 6 10091 - 1 - 1
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
An ordinary (Fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 7. Event B: The sum is divisible by 4...