Probability
Two Dice Sum — Conditional Probability Inequality
nta_pyq_2023_apr
Grade 12
Question:
Let $N$ be the sum of two dice. If $P(2^N<N!)=\dfrac{m}{n}$ (coprime), then $4m-3n$ is equal to
Step-by-Step Solution
Key Concept: $2^N<N!$ fails for $N=2$ ($4<2$: false), $N=3$ ($8<6$: false), $N=4$ ($16<24$: true!). Actually $2^2=4>2!=2$, $2^3=8>3!=6$, $2^4=16<24$. So condition holds for $N\geq4$.
$m=11,n=12$. $4m-3n=8$.
Correct Answer: 4