Question 1: Place the following events on the probability scale from 0 to 1: (a) Rolling a sum of 7 with two dice, (b) Winning a lottery with a 1 in 1000 chance, (c) Getting heads when flipping a fair coin.

Answer: [a] 0.167 [b] 0.001 [c] 0.5

Question 2: Calculate the probability that an event with a likelihood of 0.2 is placed correctly on the scale. Show your working.

Answer: 0.2

Question 3: A biased spinner has a 0.3 probability of landing on red. Plot this event on the probability scale.

Answer: 0.3

Question 4: Construct a probability distribution for drawing a card from a standard deck where the event is drawing a king. Place this event on the scale.

Answer: 4/52 ≈ 0.077

Question 5: A bag contains 3 blue, 2 red, and 5 green balls. Place the event 'drawing a red ball' on the probability scale and calculate its value.

Answer: 2/10 = 0.2

Question 6: Explain why an impossible event is placed at 0 and a certain event at 1 on the scale. Provide an example for each.

Answer: Impossible event example: drawing a 7 on a single six-sided die (place at 0). Certain event example: drawing a card from a deck and getting a card (place at 1).

Question 7: A weather forecast states the chance of rain tomorrow is 0.4. Plot this probability on the scale and justify your placement.

Answer: 0.4

Question 8: A game has a 0.05 probability of winning a jackpot. Place this event on the probability scale and discuss whether it is considered likely or unlikely.

Answer: 0.05; unlikely

Question 9: A coin is biased with a 0.6 chance of landing tails. Plot this event on the scale and compare it to a fair coin.

Answer: 0.6

Question 10: Identify a common mistake when placing a probability of 0.8 close to 1 on the scale and explain how to correct it.

Answer: Misplacing 0.8 too close to 1 without considering the decimal accuracy; correct by ensuring 0.8 is clearly less than 1 and on the appropriate point.