please answer 5

Question 3 (1 point) s/ Saved Two siblings are put in separate rooms and are asked to simultaneously write down a number on separate pieces of paper and hand it over to a parent. Only the numbers 1,2, and 6 are allowed. If the numbers match, the siblings each gets that number of chocolate bars. If the numbers do not match, the siblings do not get any chocolate bars. If a sibling receives x chocolate bars, his or her utility is x. Consider the following statement: "In any pure-strategy NE, the siblings write down the same number". Is this statement true or false? Question 4 (2 points) ~/ Saved Consider the sibling game again. There is a mixed-strategy NE in which the siblings randomize over all three numbers (1, 2 and 6). Derive this equilibrium. In this NE, what is the probability that any given sibling writes 1 on his/her piece of paper (NB: remember how to write probabilities from the first question)? What is the probability that any given player writes 2 on his/her piece of paper? Question 5 (1 point) In the mixed-strategy NE you just derived, what is the expected number of chocolate bars that each sibling receives? As before, write only the number