Suppose you conduct an experiment where you first toss a six-sided die and then flip an unfair coin where P(H) = 0.35 and P(T) = 0.65. Construct a tree diagram to help you find the following probabilities. Round answers to three decimal places.
Suppose you conduct an experiment where you first toss a six-sided die and then flip an...
Consider the setting where you first roll a fair 6-sided die, and then you flip a fair coin the number of times shown by the die. Let D refer to the outcome of the die roll (i.e., number of coin flips) and let H refer to the number of heads observed after D coin flips. (a) Suppose the outcome of rolling the fair 6-sided die is d. Determine E[H|d] and Var(H|d). (b) Determine E[H] and Var(H).
(a) Draw a tree diagram to display all the possible outcomes
that can occur when you flip a coin and then toss a die.
(b) How many outcomes contain a head and a number greater than
4?
(c) Probability extension: Assuming the outcomes displayed
in the tree diagram are all equally likely, what is the probability
that you will get a head and a number greater than 4 when you flip
a coin and toss a die? (Round your answer...
in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game
Help Please Suppose you roll a six-sided die and flip three coins. What is the chance that the die will come up as an even number and you'll get at least one heads? Express your answer as a value between 0 and 1, rounded to two decimal places
Construct a tree diagram of a probability experiment where a 6-sided die is rolled, and then a coin is flipped. a. The probability that there was a number greater than 3 and a tail on the coin. b. The probability that there was an even number on the dies and a tail on the coin. Show all the calculation steps
Suppose you toss a six-sided die 10 times. What is the probability of never rolling a 3? Round to four decimal places.
Draw a tree diagram displaying all possible outcomes given a roll of a six sided die, a coin flip, then a second coin flip. Examples of possible outcomes are 5H H meaning a roll of a , then a Heads, and a Heads TH meaning a roll of a 1, then a Tails, then a Heads
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 you toss a six-sided die 10 times. What is the probability of never rolling a 4?
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...