(a)(i):(1/2)^20×20C15 (ii):all equals to (1/2)^20×20C10 (b)When the remainder is a constant polynomial, there should be no terms that contain x when x^2=-a^2 due to the remainder therom. By substituting x^2=-a^2 into the function, we can see that (1-a^2)x is the only term that has x as a component. Therefore, when the term =0, the remainder would be a constant polynomial. Hence, when finding probability that the remainder is a constant polynomial, only x=0 or x^2=-1(rej) should be considered.

a) 點解咁鍾意將m1嘅binomial distribution溝埋core 好肯定Core唔會咁樣問，雖然CoreMC有出過binom distribution😂😂 a(i) = 20C15×0.5^15×(1-0.5)^5 (ii) For mean, Note P1+P2+...+P21 = 1, Mean=1÷21 Note 20Cn increases when n increases from 0 to 10 and decreases when n decreases from 10 to 20, Maximum= 20C10 × 0.5^10 × (1-0.5)^10 Median= P5 = P15 = 20C5 × 0.5^5 × (1-0.5)^15 有錯請指正🙏🏻