You roll one blue 6-sided die, and one red 4-sided die. Let A be the event...

You roll one blue 6-sided die, and one red 4-sided die. Let A be the event that the outcome of the red die is twice the outcome on the blue die Let B be the event that the outcome of the blue die is greater than the outcome on the red die Let C be the event that the sum of the two dice is a prime number. a) Find P(B) and P(C) by clearly listing all outcomes in B and C. b) Are the events A and C C mutually exclusive? Clearly justify your answer. c) You throw the pair of dice until event B occurs. What is the expected number of throws it takes for B to occur for the first time? (You may use any known distribution results and any results from a-c, clearly identify distribution)

Expert Solution

orchestra answered 2 years ago

You roll two 6-sided dice numbered 1 through 6. Let A be the event that the...

You roll two 6-sided dice numbered 1 through 6. Let A be the event that the first die shows the number 3, let B be the event that the second die shows a 5, and let E be the event that the sum of the two numbers showing is even. Compute P(A)and P(B)and then compute P(AlB). What does this tell you about events A and B?Hint: Remember that the sample space has 36 outcomes! Compute P(ElA)and compute P(E). What does...

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled....

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled. Let - X1 be the random variable which is 1 if the numbers rolled on the blue die and the yellow die are the same and 0 otherwise; - X2 be the random variable which is 1 if the numbers rolled on the red die and the yellow die are the same and 0 otherwise; - X3 be the random variable which is 1...

PROJECT C Roll a 6-sided die 800 times. If you do not desire to roll a...

PROJECT C Roll a 6-sided die 800 times. If you do not desire to roll a die manually, STATDISK can be used to simulate the process. To use STATDISK, go to “Data” at the top of the STATDISK window, and then choose “Dice Generator”. The “Dice Roll Random Sample Generator” window will appear. Then in that window, put 800 in for “Sample Size”, put 1 in for “Num Dice”, and put 6 in for “Num Sides”. Please disregard the “Random...

Let ? be the number that shows up when you roll a fair, six-sided die, and,...

Let ? be the number that shows up when you roll a fair, six-sided die, and, let ? = ?^2 − 5? + 6. a. Find both formats for the distribution of ?. (Hint: tep forms of probability distributions are CDF and pmf/pdf.) b. Find F(2.35)

Suppose a 9-sided and a 4-sided die are rolled. Find these probabilities. a. P(roll sum of...

Suppose a 9-sided and a 4-sided die are rolled. Find these probabilities. a. P(roll sum of less than 5 or roll doubles) b. P(roll a sum greater than 6 for the first time on the sixth roll)

Roll two fair dice. Each die has six faces. A. Let A be the event that...

Roll two fair dice. Each die has six faces. A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) = Round your answer to two decimal places. B. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to two decimal places. C. Are A and B mutually exclusive events? (Yes or No) D. Are A and B independent or...

The newest invention is a three-sided die. On any roll of this die, the result is...

The newest invention is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. A. Find the probability that exactly two of the rolls result in a 3. B. Given that exactly two of the six rolls resulted in a 1, find the probability that the first roll resulted in a 1. C. We are...

1. Players A and B each roll a fair 6-sided die. The player with the higher...

1. Players A and B each roll a fair 6-sided die. The player with the higher score wins £1 from the other player. If both players have equal scores, the game is a draw and no one wins anything. i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X). ii. What is the conditional probability that player A rolls a 2...

You have 2 fair six-sided dice: one that is red and one that is blue. You...

You have 2 fair six-sided dice: one that is red and one that is blue. You conduct a random experiment by rolling the red die first and then rolling the blue die. Use this information and answer questions 2a to 2e. 2a) Determine whether following statements are outcome or event. You roll a red 1 and blue 3. You roll a red 2 and blue 5. The sum of two dice is greater than 9. 2b) How many outcomes are there...

Suppose that you are offered the following "deal." You roll a six sided die. If you...

Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $15. If you roll a 3, 4 or 5, you win $1. Otherwise, you pay $4. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table X P(X) b. Find the expected profit. $ ____ (Round to the nearest cent) c....

Question