★ Q12 — Five sample-space investigations
Write a suitable sample space and find each probability: (i) two fair dice have a prime sum greater than 5; (ii) two different colours from 4R, 3G, 2B without replacement; (iii) three fair coins start with H and show exactly two heads; (iv) a uniformly chosen permutation of 1,2,3,4 is even; (v) independent uniform guesses on three four-option questions give exactly two correct answers. Coins and dice are independent.