Question 1: List all possible outcomes when flipping a coin and rolling a six-sided die. Ensure your list is systematic and complete.

Answer: HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6

Question 2: A student attempts to list outcomes for drawing a card from a standard deck and spinning a spinner with outcomes A, B, C. They mistakenly omit some outcomes. Identify and correct the mistake in their list.

Answer: Possible mistake: Omitting some suits or spinner outcomes; correction: list all 52 cards with each spinner outcome for each card.

Question 3: Construct a systematic list of all two-letter combinations using the letters A, B, and C. The list should be complete and without repetitions.

Answer: AA, AB, AC, BA, BB, BC, CA, CB, CC

Question 4: A common error when listing outcomes for drawing two socks from a drawer containing red and blue socks is to miss some combinations. Explain the error and list all correct outcomes systematically.

Answer: Error: Missing outcomes like red-red or blue-blue; correct list: RR, RB, BR, BB.

Question 5: List all possible outcomes when selecting a fruit from a basket containing apples, oranges, and bananas, and then choosing a drink: tea or coffee. Ensure your list is systematic.

Answer: Apple-Tea, Apple-Coffee, Orange-Tea, Orange-Coffee, Banana-Tea, Banana-Coffee

Question 6: A student lists outcomes for two dice but repeats some outcomes or omits others. Describe a common mistake in systematic listing and provide a correct list for the sums resulting from two dice.

Answer: Mistake: Repeating outcomes like (3,4) and (4,3) separately when only sums are needed; correct list of sums: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Question 7: Construct a systematic list of all three-digit numbers using digits 1, 2, and 3, without repetitions within each number.

Answer: 123, 132, 213, 231, 312, 321

Question 8: Explain the error made when listing outcomes for selecting two books from a set of three books labeled X, Y, Z, and how to correct it.

Answer: Error: Listing only ordered pairs (X,Y) but missing combinations like (Y,X); correction: list all unordered pairs or ordered pairs, depending on context.

Question 9: List all possible two-letter arrangements from the letters D, E, F where no letter is repeated in each arrangement.

Answer: DE, DF, ED, EF, FD, FE

Question 10: A student attempts to list outcomes when choosing a shirt and pair of trousers from three options each, but they include duplicates. Identify the mistake and produce a correct systematic list.

Answer: Mistake: Including pairs like (Shirt 1, Trousers 1) twice; correct list: list each shirt with each pair of trousers once.

Question 11: Using the set {A, B, C, D}, list all possible outcomes for selecting two different letters, ensuring no repetitions and order matters.

Answer: AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC

Question 12: A student tries to list outcomes for choosing one fruit from apples, bananas, and cherries, and one drink from tea, coffee, and juice. They forget some combinations. List all correct outcomes systematically.

Answer: Apple-Tea, Apple-Coffee, Apple-Juice, Banana-Tea, Banana-Coffee, Banana-Juice, Cherry-Tea, Cherry-Coffee, Cherry-Juice