3. (a) (i) A mission to Mars will consist of a team of 4 astronauts randomly selected from a group of 14 available astronauts. Exactly 5 of the 14 astronauts are trained Engineers. What is the probability that the mission will contain a team with at least 2 trained Engineers? [5 marks] (ii) Consider throwing two fair dice. What is the probability that neither a double (two dice have same number) nor a sum of 8 will appear? [5 marks] (b) A bag contains 4 coins: two regular coins (where probability of landing heads P(H)=0.5), one two-headed coin (where probability of landing heads P(H) = 1) and one cheaters coin with P(H) = 0.75. (i) You pick a coin at random and toss it once. What is the probability that it lands head? [6 marks] (ii) You pick a coin at random and toss it once, and get head. What is the probability that it is the two-headed coin? [4 marks]