Decision Making Flashcards

A spinner has 8 equal sections numbered 1–8. What is the probability of spinning an odd number greater than 3?

Answer: 1/4

Odd numbers greater than 3: 5, 7 — two outcomes. Probability = 2/8 = 1/4.

'Some athletes are vegetarian. All vegetarians avoid red meat.' Which conclusion is valid?

Answer: Some athletes avoid red meat

The overlap between athletes and vegetarians means some athletes (those who are vegetarian) also avoid red meat. 'All' and 'No' are too strong given 'some'.

A table shows sales data. Year 1: £120k, Year 2: £150k, Year 3: £180k. What is the percentage increase from Year 1 to Year 3?

Answer: 50%

Increase = £180k − £120k = £60k. Percentage = (60/120) × 100 = 50%.

Two dice are rolled. What is the probability both show a 6?

Answer: 1/36

P(6 on die 1) × P(6 on die 2) = 1/6 × 1/6 = 1/36. Independent events multiply.

A logical argument: 'All managers approve budgets. James does not approve budgets.' What follows?

Answer: James is not a manager

Modus tollens: if all managers approve budgets (M→B), and James does not approve budgets (¬B), then James is not a manager (¬M).

A hospital has 3 wards. Ward A has 40 patients, Ward B has 35, Ward C has 25. A random patient is selected. What is the probability they are from Ward B?

Answer: 35/100

Total patients = 100. P(Ward B) = 35/100 = 7/20. Both 35/100 and 7/20 are equivalent; 35/100 is the direct calculation.