Hi, I am in difficulty when I kept trying to do these questions.

Could you give me a help to solve these questions?

Thank you so much.

In a carnival game, a player rolls two 6-sided dice. - If the two dice land on the same value (ex. (1,1), (2,2), etc), the player wins $20. - If the sum of the two values is odd (ex. (1,4), (5,2), (3,6), etc}, the player loses $10. - If both dice have odd values that are different (ex. (1,3), (5,3). (1,5), etc), the player wins $3. - If both dice have even values that are different (ex. (4,2), (4,6), (6,2), etc), the player loses $5. (a) Create the probability mass function (pmf) for X. Provide enough justication in your work to make it clear how each probability was calculated. (b) Determine V[X]. (c) Determine V[45 6X]. A company sells tiny batteries for hearing aids. They advertise that 80% of their batteries last at least 7 days, and they sell their batteries in boxes of 10. Assume that the lifespans of individual batteries are independent of one another. (a) What is the probability that at least three of the batteries in a random box of 10 will last less than 7 days? {b} A box of batteries is considered to be \"below-standard" if at least three of the ten batteries last less than 7 days. If ve random boxes are tested, what is the probability that exactly one of the boxes is deemed below-standard? Assume that the standard of boxes of batteries are independent of one another. (c) Out of the ve boxes in part (b), how many boxes are expected to be below-standard