Decision Making Flashcards

A bag contains 3 red, 4 blue, and 5 green balls. If one ball is drawn at random, what is the probability it is NOT green?

Answer: 7/12

Total balls = 12. Non-green = 3 + 4 = 7. Probability = 7/12.

A company has 5 managers and needs to select a team of 2. How many different teams are possible?

Answer: 10

Combinations: C(5,2) = 5!/(2!×3!) = 10. Order does not matter for team selection.

In a survey, 60% of people own a car, 40% own a bike, and 25% own both. What percentage own neither?

Answer: 25%

By inclusion-exclusion: car or bike = 60 + 40 − 25 = 75%. Neither = 100 − 75 = 25%.

All doctors are professionals. Some professionals work long hours. Which conclusion must be true?

Answer: Some doctors may work long hours

Since some professionals work long hours and all doctors are professionals, it is possible (but not certain) that some doctors work long hours. The word 'must' makes only the weakest provable claim valid.

A train travels at 80 km/h for the first half of a journey and 120 km/h for the second half (equal distances). What is the average speed?

Answer: 96 km/h

Harmonic mean for equal distances: 2×(80×120)/(80+120) = 2×9600/200 = 96 km/h. The arithmetic mean (100) is wrong when speeds cover equal distances.

Four friends — A, B, C, D — sit in a row. A must not sit next to D. How many valid arrangements are there?

Answer: 12

Total arrangements = 4! = 24. Arrangements where A sits next to D: treat AD as a block → 3! × 2 = 12. Valid = 24 − 12 = 12.