Question

A 10 sided die with sides numbered 0 through 9 is rolled 5 times. Let X...

A 10 sided die with sides numbered 0 through 9 is rolled 5 times. Let X be the number of zeros rolled.
(a) Find the probability that exactly 2 zeros are rolled.
(b) Find the probability that no less than 4 zeros are rolled.
(c) Find the mean and the variance of X.

Homework Answers

Answer #1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 1/10 = 0.1

N = number of trials = 5

R = desired success

A)

P(2) = 5c2*(0.1^2)*(1-0.1)^5-2 = 0.0729

B)

P(4) + P(5)

= 0.00046

C)

Mean = n*p = 5*0.1 = 0.5

Variance = n*p*(1-p) = 5*0.1*0.9 = 0.45

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A balanced die with 10 ​sides, numbered 1 through 10​, is rolled 100 times. a. For...
A balanced die with 10 ​sides, numbered 1 through 10​, is rolled 100 times. a. For the binomial distribution of X = number of 10​s, what is n and what is​ p? b. Find the mean and the standard deviation of the distribution of X. Interpret. c. If you observe x = ​0, would you be skeptical that the die is​ balanced? Explain​ why, based on the mean and standard deviation of X. d. Find the probability that x =...
5. If a four-sided die is rolled 9 times, what is the probability of getting exactly...
5. If a four-sided die is rolled 9 times, what is the probability of getting exactly four 2s? A. ≈ .0009 B. ≈ .0389 C. ≈ .0751 D. ≈ .1168 E. other value 6. If a four-sided die is rolled, find the standard deviation of the number showing. (Hint: First find the variance.) A. ≈ 1.12 B. ≈ 1.25 C. ≈ 2.50 D. ≈ 7.5 E. other value 7. If a die is rolled 36 times, approximate the probability of...
1) A 10-sided die is rolled infinitely many times. Let X be the number of rolls...
1) A 10-sided die is rolled infinitely many times. Let X be the number of rolls up to and including the first roll that comes up 2. What is Var(X)? Answer: 90.0 2) A 14-sided die is rolled infinitely many times. Let X be the sum of the first 75 rolls. What is Var(X)? Answer: 1218.75 3) A 17-sided die is rolled infinitely many times. Let X be the average of the first 61 die rolls. What is Var(X)? Answer:...
A die is rolled six times. (a) Let X be the number the die obtained on...
A die is rolled six times. (a) Let X be the number the die obtained on the first roll. Find the mean and variance of X. (b) Let Y be the sum of the numbers obtained from the six rolls. Find the mean and the variance of Y
You have a 4 sided die and 10 sided die that are rolled 50 times. What...
You have a 4 sided die and 10 sided die that are rolled 50 times. What is the theoretical probability that the small die is odd, the sum of the numbers is 5, the same # appears on both, the # on the larger die is > than the # on the smaller die.
Assume that a fair six-sided die is rolled 9 times, and the roll is called a...
Assume that a fair six-sided die is rolled 9 times, and the roll is called a success if the result is in {1,2}{1,2}. What is the probability that there are exactly 4 successes or exactly 4 failures in the 9 rolls?
You have a fair five-sided die. The sides of the die are numbered from 1 to...
You have a fair five-sided die. The sides of the die are numbered from 1 to 5. Each die roll is independent of all others, and all faces are equally likely to come out on top when the die is rolled. Suppose you roll the die twice. Let event A to be “the total of two rolls is 10”, event B be “at least one roll resulted in 5”, and event C be “at least one roll resulted in 1”....
A fair six-sided die is rolled 10 independent times. Let X be the number of ones...
A fair six-sided die is rolled 10 independent times. Let X be the number of ones and Y the number of twos. (a) (3 pts) What is the joint pmf of X and Y? (b) (3 pts) Find the conditional pmf of X, given Y = y. (c) (3 pts) Given that X = 3, how is Y distributed conditionally? (d) (3 pts) Determine E(Y |X = 3). (e) (3 pts) Compute E(X2 − 4XY + Y2).
A six-sided die is rolled 10 times and the number of times the six is rolled...
A six-sided die is rolled 10 times and the number of times the six is rolled is recorded. This is an example of a binomial experiment. Select one: True False
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than...
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than or equal to 4 is rolled once again. Let X be the number of dice that show a number less than or equal to 4 on the first roll, and let Y be the total number of dice that show a number greater than 4 at the end. (a) Find the joint PMF of X and Y . (Show your final answer in a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT