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?