Question 1: A class of 30 students is to be randomly sampled to select 5 students for a survey. If all students have an equal chance of being selected, what is the probability that a specific student is chosen?

Answer: 5/30 or 1/6

Question 2: Calculate the probability of selecting exactly 2 girls from a class of 12 students (6 boys and 6 girls) when 4 students are randomly sampled without replacement.

Answer: 15/66

Question 3: In a bag of 50 marbles, 20 are red and 30 are blue. If 5 marbles are randomly drawn, what is the probability that all 5 are blue?

Answer: C(30,5)/C(50,5)

Question 4: Explain why simple random sampling ensures each individual in a population has an equal chance of being selected. Provide a brief reasoning.

Answer: Because each individual is assigned an equal chance, and the selection process is random, ensuring fairness and no bias.

Question 5: A researcher randomly samples 15 students from a school with 200 students. If the sample includes 8 boys and 7 girls, what is the probability that a randomly selected student from this sample is a girl?

Answer: 7/15

Question 6: A survey is conducted by randomly selecting 100 people from a city's population. How many people are expected to be selected if the probability of choosing any individual is uniform? Explain your reasoning.

Answer: All 100 individuals are potential candidates; the expected number depends on the sampling method, but in simple random sampling, all have an equal chance.

Question 7: Construct a scenario where random sampling could lead to bias. Briefly describe the situation.

Answer: If the sampling frame excludes certain groups (e.g., only sampling from online lists), it can lead to bias.

Question 8: Calculate the probability of not selecting any red marbles if 3 marbles are randomly drawn from a bag containing 10 red and 40 blue marbles.

Answer: (C(40,3)/C(50,3))

Question 9: Identify and correct the mistake: A student claims that in random sampling, choosing the same individual twice is acceptable and does not affect the probability.

Answer: Mistake: In random sampling without replacement, selecting the same individual twice is not possible or should be ignored; it affects probabilities.

Question 10: A random sample of 50 students is taken from a school of 600 students. If 25 of these students own a laptop, what is the probability that a randomly selected student from the sample owns a laptop?

Answer: 25/50 or 1/2

Question 11: In a class of 40 students, 10 are absent on a day when a random sample of 8 students is selected. Does this affect the probability calculations? Explain briefly.

Answer: Yes, absenteeism affects the sampling if the sample is taken without accounting for absences, potentially biasing results.