Solution:
Suppose that a balanced, six-sided die has been altered so that the faces are 1, 2,...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die lands with...
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the uppermost face. Given N, a fair coin is tossed independently until N heads are recorded. Let X be the total number of tails recorded. a. What is the pmf of N? (5 pts) b. Given N = 3, what is the distribution of X? (10 pts) c. What is Pr(X = 1)? (10 pts) d. What is E(X)? (10 pts)
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/3. C_2 will land Heads with probability 1/5. C_3 will land Heads with probability 1/4. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die...
Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a 1 face up, flip coin C_1 If the die...
PLEASE SHOW EACH STEP- SHOW THE PROBABILITY WITH FRACTIONS A fair six-sided die has faces numbered 1 through 6. A) What is the probability that the die would be rolled 3 times in order to get the first 2? B) What is the probability that the die would be rolled 4 times in order to get the first odd number?
Please answer all parts to this 4 part question Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C_1, C_2, and C_3. C_1 will land Heads with probability 1/5. C_2 will land Heads with probability 1/3. C_3 will land Heads with probability 1/2. You roll the die. If the die lands with a...
Two faces of a six-sided die are painted red, two are painted brown, and two are painted green. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) What is the probability that the three rolls produce exactly two different colors? (b) What is the probability that the three rolls produce at least one red?
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.
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...