Question

Howard rolls a fair, 6 sided die 6 times. He is recording how many times he...

Howard rolls a fair, 6 sided die 6 times. He is recording how many times he rolls a multiple of 3. What is the probability of Howard rolling exactly 3 multiples of 3? Show your work.

Homework Answers

Answer #1

If a 6 sided die is rolled, then in 2 ways it can be multiple of 3, one is if 3 is rolled, another is if 6 is rolles. And in a die total number of possible outcome is 6. So if getting a number multiple of 3 is defined as success, then success probability, p =2/6 =1/3

Failure probability, q=2/3

Total number of trial, n=6

Number of success=3

Let Number of times Howard gets a amultiple of 3 is denoted by a random variable X.

X~ Bin(6, 1/2)

So, P(X=3)= (2/3)^(6-3)*(1/3)^3= 0.2195

The probability that Howard gets multiple of 3 exactly 3 times is 0.2195.

Please support me by putting thumbs up. Thank you.

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
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:...
5. Suppose the six-sided die you are using for this problem is not fair. It is...
5. Suppose the six-sided die you are using for this problem is not fair. It is biased so that rolling a 6 is three times more likely than any other roll. For this problem, the experiment is rolling a six-sided die twice. (A): What is the probability that one or both rolls are even numbers (2, 4 or 6’s)? (B): What is the probability that at least one of the rolls is an even number or that the sum of...
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?
1. Suppose you have a fair 6-sided die with the numbers 1 through 6 on the...
1. Suppose you have a fair 6-sided die with the numbers 1 through 6 on the sides and a fair 5-sided die with the numbers 1 through 5 on the sides. What is the probability that a roll of the six-sided die will produce a value larger than the roll of the five-sided die? 2. What is the expected number of rolls until a fair five-sided die rolls a 3? Justify your answer briefly.
Troy is conducting an experiment. He first rolls a fair die (six-sided) and then draw a...
Troy is conducting an experiment. He first rolls a fair die (six-sided) and then draw a chip out of a box containing 2 red chips, 4 green chips, and 9 blue chips. What is the probability Troy will roll a 3 and then draw a green chip?
A fair 4-sided die and a fair 6-sided die will be rolled. A) Give the sample...
A fair 4-sided die and a fair 6-sided die will be rolled. A) Give the sample space. B) What is the probability the sum is 9? C) What are the chances that the sum is 4, or the 4 sided die comes up a 3?
A fair 4-sided die is rolled 7 times. (a) Find the probability that the side 1...
A fair 4-sided die is rolled 7 times. (a) Find the probability that the side 1 comes up exactly 3 times. (b) Find the probability that there is at least one side that comes up exactly 3 times.
Suppose you plan to roll a fair six-sided die two times. What is the probability of...
Suppose you plan to roll a fair six-sided die two times. What is the probability of rolling a ‘1’ both times? Group of answer choices
Suppose you roll a single fair die 10 times (all rolls are mutually independent). What is...
Suppose you roll a single fair die 10 times (all rolls are mutually independent). What is the probability that you roll a 5 in exactly 3 of the 10 rolls?
Imagine rolling two fair 6 sided dice. What is the probability the number rolled on the...
Imagine rolling two fair 6 sided dice. What is the probability the number rolled on the first die is even or the sum of the rolls is 10?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT