ITPEC FE Morning April 2023 Question 4

Probability with Random Functions — calculate P(C = 0) where C = A − B.

Random(10) returns integers 0..9 uniformly. C = A − B = 0 when A == B.

• •Total outcomes: 10 × 10 = 100
• •Favorable outcomes (A = B): (0,0), (1,1), …, (9,9) → 10
• •Probability: 10 / 100 = 1/10

Why not others:
- (a) 1/100 — probability of one specific pair, not all matching pairs
- (b) 1/20 — no combinatorial basis
- (d) 1/5 — no combinatorial basis

Key rule: When two independent uniform random variables have the same range of n values, P(A = B) = n / n² = 1/n.

AI-generated — may contain errors