1. A lottery consists of 49 balls numbered 1 through 49 and 6 of them are drawn at random.

(a) You can pick 6 different numbers for a betting ticket. How many selections are possible?

(b) If prizes will be paid to those picking 4 to 6 drawn numbers, how many winning selections are possible?

2. Asian Hong Kong airlines Company plans to randomly select total 100 passengers to join the customer satisfaction survey from different countries in Asia in the period of December 2021. According to the airline database, there were 300 passengers from Hong Kong, 200 passengers from mainland China, 200 passengers from Japan, 150 passengers from South Korea and 150 passengers from Thailand during the period.

(a) Identify the sampling method used in the above situation.

(b) State ONE advantage of this sampling method.

(c) How many passengers from Japan should be selected for the survey?

3. In a football match, the winner gets 2 points and loser gets no point. If the match ends in a draw, then both get 1 point. A football team joins the match and the probability that the team can win the match is 0.5 and lose the match is 0.3.

(a) Find the probability that the match ends in a draw.

(b) Calculate the expected point that the team will get in the match.