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ETC2420 - ETC5242 - Statistical thinking - S2 2026
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Create a new variable called Grade that categorises Exam score into:
- Less than 50: "N",
- From 50 to below 60: "P",
- From 60 to below 70: "C",
- From 70 to below 80: "D",
- All other scores: "HD"
For a group of 10 people, the probability that no two people share a birthday is approximately 0.883 (assuming birthdays are equally likely across 365 days and ignoring leap years). Using the complement rule, what is the approximate probability that at least two people in the group of 10 share a birthday?
Three fair six-sided dice are rolled. It turns out that the unordered combinations that sum to 11 and the unordered combinations that sum to 12 both consist of exactly 6 distinct combinations of numbers. However, there are 27 ordered outcomes (out of 216 total) that sum to 11, and 25 ordered outcomes that sum to 12. What is the probability that the sum of the three dice is 11?
A household has two pets. Each pet is independently a dog or a cat, each with probability 1/2, and the type of one pet does not affect the other. Given that at least one pet is a dog, what is the probability that both pets are dogs?
A city council needs to select 4 members from a pool of 15 candidates to form a subcommittee. The four selected members have no distinct roles — they simply form an unordered group of 4. How many different subcommittees are possible?
An investor puts money into one of five roughly similar start-ups. Two years later, that start-up has tripled in value while the other four have folded. The investor says:
"I knew it would be the winner. It was obviously the best choice."
Which statement best explains the flaw in this reasoning?
A carnival wheel is divided into four coloured segments of different sizes, so the segments are not equally likely to be landed on. The probabilities are:
Red = 0.35,
- Blue = 0.30,
- Yellow = 0.20,
Green = ?
Since the probabilities of all possible outcomes must add to 1, what is the probability of landing on Green?
- Analyst A: "It's a toss-up."
- Analyst B: "Almost impossible."
- Analyst C: "There's a 15% chance."
- Analyst D: "Quite likely.
"
Which statement is the most precise, and why?
A cybersecurity analyst receives three independent alerts pointing to a possible breach. Each alert, considered on its own, has a 50% chance of being accurate (and therefore a 50% chance of being a false alarm).
What is the probability that at least one of the three alerts is accurate?