9. Two fair dice are rolled one thousand times. Approximate the probability that the number of...
9. Two fair dice are rolled one thousand times. Approximate the probability that the number of aces (two numbers six) is between 25 and 31 (inclusive). Use DeMoivre-Laplace approximation with continuity correction.
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
1. An eight-sided dice is rolled 24 times a) What is the expected number of times the dice shows 8? b) What is the probability that the dice shows a 8 the ex- pected number O (c) Using a normal approximation for the binomial distribu tion estimate the probability of rolling 8 six or more times
4. Two fair dice are rolled. Compute the probability that the number on the first is smaller than the number on the second
Three six-faced fair dice are rolled. What is the probability that exactly two of the dice have the face value of 6?
A fair die is rolled. What is the probability of the dice coming up a one or a six? Your workings should show the use of appropriate laws and formulae — do not provide a purely arithmetic answer.
I know Pk~1/k^5/2 just need the work Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
If two fair dice are rolled, what is the conditional probability that the rst one lands on an even number given that the second one lands on a number less than or equal to four? Compute the conditional probability that the second one lands on a number less than four given that the rst one lands on an even number.
A fair pair of dice is rolled 36 times. Find the probability that the same point comes up on both dice at least 11 times
1) If a fair die is rolled 25 times, what is the probability that a 3 is obtained exactly 3 times? Round your answer to the nearest thousandth. Use 1/6 as 0.167 in your calculations. 2) If X has a geometric distribution with parameter p = 0.523, calculate p(X=8) Round your answer to the nearest thousandth. 3) The number of imperfections in an object has a Poisson distribution with a mean λ = 8.3. If the number of imperfections is...