Example 4: A fair six-sided die is rolled six times. If the face numbered k is...

Example 4: A fair six-sided die is rolled six times. If the face numbered k is the outcome on roll k for k = 1, 2, 3, 4, 5, 6 we say that a match has occurred. The experiment is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The outcome space is O = {success, failure}. Let event A = {success}. Which value has P(A)?

**This question has been posted a few times on here, but the answers were not good explanations**

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6...

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6 together. After rolling both dice, let X denote the number appearing on the foursided die and Y the number appearing on the six-sided die. Define W = X +Y . Assume X and Y are independent. (a) Find the moment generating function for W. (b) Use the moment generating function technique to find the expectation. (c) Use the moment generating function technique to find...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X is the number appearing on the four-sided die and Y is the number appearing on the six-sided die. Define W=X+Y when they are rolled together. Assuming X and Y are independent, (a) find the moment generating function for W, (b) the expectation E(W), (c) and the variance Var(W). Use the moment generating function technique to find the expectation and variance.

A six sided die is rolled 4 times. The number of 2's rolled is counted as...

A six sided die is rolled 4 times. The number of 2's rolled is counted as a success. Construct a probability distribution for the random variable. # of 2's P(X) Would this be considered a binomial random variable? What is the probability that you will roll a die 4 times and get a 2 only once? d) Is it unusual to get no 2s when rolling a die 4 times? Why or why not? Use probabilities to explain.

A six sided die is rolled 4 times. The number of 2's rolled is counted as...

A six sided die is rolled 4 times. The number of 2's rolled is counted as a success. Construct a probability distribution for the random variable. # of 2's P(X) Would this be considered a binomial random variable? What is the probability that you will roll a die 4 times and get a 2 only once? d Is it unusual to get no 2s when rolling a die 4 times? Why or why not? Use probabilities to explain.

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...

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 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...

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.

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

a fair 6-sided die is rolled three times. What is the probability that all three rolls...

a fair 6-sided die is rolled three times. What is the probability that all three rolls are 2? Round the answer to four decimal places

Subjects