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1. Suppose a fair six-sided die is tossed, with N being the resulting number on the...
A fair (6-sided) die is rolled once, generating a number N. If the number N is even, then a fair coin is tossed N + 1 times. If the number N is odd, then a fair coin is tossed 2N times. Let X be the number of heads obtained. Compute E(X). Give a numerical answer as a reduced fraction or a decimal expression accurate to at least 4 decimal places.
3. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2? A. 1/2 B. 1/4 C. 1/6 E. 1/3
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...
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...
Suppose that a balanced, six-sided die has been altered so that the faces are 1, 2, 3, 4, 5, and 5. If the die is tossed five times, and the number on the uppermost face is recorded each time, what is the probability that the numbers recorded are 1, 2, 3, 4, and 5 in any order? (Round your answer to four decimal places.)
4. A fair two-sided coin is tossed repeatedly. (a) Find the expected number of tails until the first head is flipped. (b) Find the probability that there are exactly 5 heads in the first 10 flips. (c) Use the central limit theorem/normal approximation to approximate the probability that in the first 100 flips, between 45 and 55 of the flips are heads.
In a game, a single event consists of fair six-sided die begin thrown followed by flip of a fair two-sided coin. a. state the number of possible outcome in the sample space b. find the probability that a single randomly-selected turn will be include the coin toss coming up "heads" c.find the probability that a single randomly - selected turn in include a "6" coming up on the die d.find the probability that a single randomly-selected turn will include a...
A fair coin is tossed until heads appears four times. a) Find the probability that it took exactly 10 flips. b) Find the probability that it took at least10 flips. c) Let Y be the number of tails that occur. Find the pmf of Y.