Question

In: Math

Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For...

Two 6-sided dice are rolled. Let X be the larger of the two numbers showing. For each i from 1 to 6, find the probability that X = i.

Solutions

Expert Solution

Solution:

Given: Two 6-sided dice are rolled.

X = the larger of the two numbers showing.

For example: ( 2 , 1 ) then X = 2

( 3 , 3 ) , then X = 3

and so on.

Sample space of rolling of two dice is:

We have numbers from 1 to 6 on each die, then minimum possible value for X is 1 and maximum possible value would be 6.

Now we need to find counts for each largest number.

X=i Outcomes: f : frequency Calculations: P(X=i)
1 (1,1) 1 =1/36 0.0278
2 (1,2) , (2,2) , (2,1) 3 =3/36 0.0833
3 (1,3) , (2,3) , (3,3 ), (3,2 ), (3,1) 5 =5/36 0.1389
4 (1,4) , (2,4) , (3,4 ), (4,4 ) , (4, 3 ),
(4, 2) ,(4 , 1)		 7 =7/36 0.1944
5 (1,5) , (2,5) , (3,5 ), (4,5 ) ,(5,5 ) ,
(5, 4 ), (5, 3) ,(5 ,2), (5,1)		 9 =9/36 0.2500
6 (1,6) , (2,6) , (3,6 ), (4,6 ) ,(5,6 ) ,(6,6) ,
(6, 5 ), (6, 4) ,(6,3) , (6 ,2), (6,1)		 11 =11/36 0.3056
N = 36

milcah answered 2 years ago
Next > < Previous

Related Solutions

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of...
Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of the two numbers obtained and Y the smaller of the two numbers obtained. Determine probability mass functions for X and Y, and the cumulative distribution functions for X and for Y. Present the two cumulative distribution functions in a plot. Calculate E (2X + 2Y −8).
1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the...
1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the range of X and compute P(X = 18) and P(X ≤ 4). 2. An urn contains 5 red balls and 3 green balls. (a) Draw 3 balls with replacement. Let X be the number of red balls drawn. Determine the range of X and compute P(X = 3) and P(X 6= 1). (b) Draw 3 balls without replacement. Let Y be the number of...
One red (6 sided) and one white (6 sided) dice is rolled. The random variable X...
One red (6 sided) and one white (6 sided) dice is rolled. The random variable X has the value 1 if the red dice shows a number max 2 and is 2 else. The random variable y has the value 1 if the white dice shows a uneven number and is 2 else. A) determine the common probability function (x, y) B) determine the marginal probability functions of x and y C) calculate e(x), e(x^2), var(x), e(y), e(y^2), and var(y)
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?
(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...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...
Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...
Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the maringals pmf's for both variables. c) Are X and Y independent?
Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers...
Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 3? What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 3? What is the probability that the sum of the numbers on the two dice is 9, given...
Two fair dice are rolled. Let X be the product of the number of dots that...
Two fair dice are rolled. Let X be the product of the number of dots that show up. (a) Compute P(X = n) for all possible values of n. (b) Compute E(X). (c) Compute Var(X) and SD(X).
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT