# Thread: probability distribution and expected value

1. ## probability distribution and expected value

I have attempted the question, but I am doubting my answer because it is a rational number and the numbers in context are not.

I am providing the whole question for context:
Two standard six-sided dice are tossed. Let X be the sum of the scores on the two dice.
(a) Find
(i) P(X=6)
(ii) P (X>6)
(iii) P(X=7 | X>5)

(b) Elena plays a game where she tosses two dice.
If the sum is 6, she wins 3 points.
If the sum is greater than 6, she wins 1 point.
If the sum is less than 6, she loses kpoints.

Find the value of k for which Elena's expected number of points is zero.

I need verification with part b).
What I did was construct a probability distribution table where X was k, 3, and 1. And my probabilities were 10/36, 5/36, 21/36, respectively. Then I set the expected value equal to zero:
(10k/36) + (3 x 5/36) + (1 x 21/36) =0
to solve for k.

I get k as -36/10.

But I'm not sure if this is right, can someone please check if my method is correct?

2. Originally Posted by bhuang

I am providing the whole question for context:
Two standard six-sided dice are tossed. Let X be the sum of the scores on the two dice.
(a) Find
(i) P(X=6)
(ii) P (X>6)
(iii) P(X=7 | X>5)

You should make a two row table. first row $x= 2,3\dots ,12$ with a second row being $P(x)$ there will be some symmetry here.

3. My probability distribution table is my two row table. Instead of 2, 3, ... I put the points obtained from the game in. It should be the same thing, right? What do you mean by symmetrical...

4. Originally Posted by bhuang
My probability distribution table is my two row table. Instead of 2, 3, ... I put the points obtained from the game in. It should be the same thing, right? What do you mean by symmetrical...
The sum of two dice can only be from 2 to 12. These are the x's.

You then need to find the probabililty of each of these occuring.

I.e $P(2) =\frac{1}{36}, P(3) =\frac{2}{36}, P(4) =\frac{3}{36}, \dots ,P(12) =\frac{1}{36}$

Do you know how I found these? After you have this information you can answer the questions.