Single fair die: P(any face) = 1/6. P(even) = 1/2. P(prime: 2,3,5) = 1/2.

Two dice: Total outcomes = 36. P(sum = 7) = 6/36 = 1/6 (highest). P(sum = 2) = P(sum = 12) = 1/36.

Coins: n fair coins: P(exactly k heads) = C$\frac{n,k}{2}$^n. P(at least one head) = 1 - $\frac{1}{2}$^n.

Common JEE setups:

• "A die is thrown n times" → Binomial with p = $\frac{desired faces}{6}$
• "Two dice are thrown" → List outcomes systematically or use complements
• "Biased coin with P(H) = p" → Binomial distribution

Useful shortcut for two dice: Number of ways to get sum s: s = 2,3,4,5,6,7,8,9,10,11,12 → ways = 1,2,3,4,5,6,5,4,3,2,1