Question

When a fair dice is rolled. 36 equally likely outcomes are possible as shown below.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let X=Max of numbers shown on the dice
a) Find the probability distribution of X. Give the probabilities rounded to three decimal places.
b) Find the mean and standard deviation of the random variable X.
c) Let A be the event that X is an even number. Find P(A)

Answer 1

i assume so... i typed it exactly as it was given to me on paper ):

Answer 2

let x=the maximum of numbers shown on the dice, i believe max means the highest number in the parenthesis for example the max of (4,3) is 4

Answer 3

oh i did make a mistake it is two fair dice

Answer 4

The first step is to make a table, listing the possible maximum numbers 1, 2, 3, 4, 5 and 6, then the number of times that number is the maximum in the 36 possible outcomes. For example 2 is the maximum number in 3 of the 36 outcomes, and 1 is the maximum number in only 1 of the 36 outcomes.

Answer 5

can you draw this out for me?

Answer 6

I think that you should make the table.

Answer 7

i dont understand how to thats why i asked...can you start out the table so i can see?

Answer 8

Max. number Number of occurrences
1 1
2 3
3 ?
4 ?
5 ?
6 ?

Answer 9

i get it! :D

Answer 10

Great!

Answer 11

3 is 5?

Answer 12

Correct.

Answer 13

okay so after im done with the table what do i do?

Answer 14

Then you need to continue the table by putting the probability of each of the maximum numbers. The probability of 1 is 1/36, the probability of 2 is 3/36, the probability of 3 is 5/36, and so on. Note: The question requires that each probability must be changed from a fraction to a decimal rounded to three places.

Answer 15

ohhh alright i uderstand, so how do i do b?

Answer 16

do i just use the # of occurrences
to find each?

Answer 17

\[\large mean=\frac{1}{36}(1\times1+2\times3+3\times5+.................+6\times11)\]

Answer 18

if thats how you find the mean then how do you find the standard deviation?

Answer 19

and is there a formula for mean?

Answer 20

Do you have a calculator with statistical functions? If you do have such a calculator are you allowed to use it to solve this question?

Answer 21

i have a TI-83

Answer 22

i can use it

Answer 23

i think i remember from high school i enter everything in list and then... idk

Answer 24

2 vars stat L1, L2?

Answer 25

My calculator is a different make. There is a Guidebook for the TI-83 here:
http://math.oregonstate.edu/home/programs/undergrad/TI_Manuals/ti83Guidebook.pdf
Pages 11-17 and 11-18 show how to find the mean and standard deviation of lists of data values.

Answer 26

thanks! :D okay last question.... for c how would i go about doing it?

Answer 27

The even maximum numbers are 2, 4 and 6. When you have completed the table, add the probabilities of 2, 4 and 6 to find the value of P(A).

Answer 28

alright! THANK YOU SO MUCH! you saved my life with this x.x

Answer 29

You're welcome:)

Answer 30

Note: When entering the list it must have 36 data values:
1, 2, 2, 2, 3, 3, 3, 3, 3,........................, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6.