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Quiz 2: Uncertainty

CS50's Introduction to Artificial Intelligence with Python

Question 1

A standard 52-card deck has 13 values in 4 suits. If a card is drawn at random, what is the probability it is a spade or a two?

  • About 0.019
  • About 0.077
  • About 0.17
  • About 0.25
  • About 0.308 ✓
  • About 0.327
  • About 0.5

Why: Use inclusion-exclusion: P(spade ∨ two) = P(spade) + P(two) − P(spade ∧ two) = 13/52 + 4/52 − 1/52 = 16/52 ≈ 0.308 The two of spades gets counted in both sets, so subtract it once.

Question 2

Flipping two fair coins, what is the probability that one lands heads and the other lands tails?

Answer: 0.5 ✓

Why: Possible outcomes: HH, HT, TH, TT — each with probability 0.25. Outcomes with one head and one tail: HT and TH = 0.25 + 0.25 = 0.5.

Question 3

From the Bayesian Network in lecture (Rain → Maintenance → Train → Appointment), which statement is true?

  • Rain affects appointment probability when train is on time
  • Maintenance affects train punctuality when rain is known
  • Rain affects train punctuality when maintenance is known
  • Assuming we know the train is on time, whether or not there is track maintenance does not affect the probability that the appointment is attended. ✓
  • Rain affects appointment when maintenance is known

Why: In a Bayesian network, once we observe a node (Train = on time), the path from its parents (Maintenance) to its children (Appointment) is blocked. This is conditional independence — knowing the train status screens off maintenance from affecting the appointment.

Question 4

Factory A produces 60% of batteries (2% defect rate). Factory B produces 40% (4% defect rate). What is the probability that a battery is both made by Factory A and defective?

Answer: 0.012 ✓

Why: P(Factory A ∧ defective) = P(defective | Factory A) × P(Factory A) = 0.02 × 0.60 = 0.012