Question

In: Statistics and Probability

If a fair coin is flipped twice and a standard 6 sided die is rolled once,...

If a fair coin is flipped twice and a standard 6 sided die is rolled once, what is the likelihood of getting two 'heads' on the coin and a '1' on the die? ​Express your answer as a percent rounded to the tenth place

Solutions

Expert Solution

Likelihood of getting two heads on coin and a 1 on the die expressed as percentage rounded to tenth place is

_____

Solution and explanation

A fair coin is flipped twice.

Since the coin is fair, probability of getting head in first flip is 1/2

probability of getting head in second flip is 1/2.

So Probability of getting two heads

Probability of getting side 1 on a six sided die in a roll is .

So the likelihood of hetting two heads on the coin and 1 on the die is

If we round this likelihood to tenth place we get


Related Solutions

We toss a fair 6 sided die and flip a fair coin twice. Define the random...
We toss a fair 6 sided die and flip a fair coin twice. Define the random variable Y1 to be the number of sports atop the die. Define Y2 to be the total number of heads obtained on the two flips of the coin. a) Find the mean value and standard deviation of Y1. b) Find the mean value and standard deviation of Y2. c) Find the mean value and standard deviation of Y1+Y2. d) What are the mean value...
A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the...
A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the sample space. S = b.{ List the following events and their probabilities. Write probabilities in non-reduced fractional form A = rolling doubles = { P(A)= / B = rolling a sum of 4 = { P(B)= / C = rolling a sum of 5 = { P(C)= C. Are the events A and B mutually exclusive? If yes, why? If not, why not? D.Are...
(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the...
(5) A fair 6-sided dice is rolled twice. The fairness of the dice consists of the following facts: (i) no face of the dice is likelier to be rolled than any other (so a roll of a 5 and a roll of a 3 are equiprobable) and (ii) the dice has no “memory” - each roll is independent of any other. 5.1: What is the probability that you’ve first rolled a 3 and the pair of rolls sums to something...
Two 6-sided dice are rolled. One die is a standard die, and the other is a...
Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. a. What is the probability distribution of this experiment? b. What is the shape of the probability distribution? c. What is the expected value when these 2 dice are rolled?
A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let...
A fair six-sided die is rolled repeatedly until the third time a 6 is rolled. Let X denote the number of rolls required until the third 6 is rolled. Find the probability that fewer than 5 rolls will be required to roll a 6 three times.
A fair die is rolled. If the result is greater than 4, a fair coin is...
A fair die is rolled. If the result is greater than 4, a fair coin is flipped, and otherwise, an unfair coin with P[H] = 2/3 is flipped. The outcome of the die roll is mapped to X, and the outcome of the coin flip is mapped to Y , with 1 for heads and −1 for tails. (a) Find the joint PMF. (b) Find both marginal PMFs. Do the marginal PMFs indicate independence?
A fair coin is tossed, and a fair die is rolled. Let H be the event...
A fair coin is tossed, and a fair die is rolled. Let H be the event that the coin lands on heads, and let S be the event that the die lands on six. Find P(H or S).
A fair six-sided green die is rolled resulting in a number between 1 and 6. Then...
A fair six-sided green die is rolled resulting in a number between 1 and 6. Then that number of red dice are rolled. Find the expected value and variance of the sum of the red dice.
A fair 6-sided die is rolled repeatedly. (a) Find the expected number of rolls needed to...
A fair 6-sided die is rolled repeatedly. (a) Find the expected number of rolls needed to get a 1 followed right away by a 2. Hint: Start by conditioning on whether or not the first roll is a 1. (b) Find the expected number of rolls needed to get two consecutive 1’s. (c) Let an be the expected number of rolls needed to get the same value n times in a row (i.e., to obtain a streak of n consecutive...
Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other...
Part 1: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. Submit a file with the probability distribution for this experiment. Part 2: Two 6-sided dice are rolled. One die is a standard die, and the other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8. What is the shape of the probability distribution? Part 3: Two 6-sided...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT