Find the probability that a randomly selected 2-digit number belongs to n N: 2^n-2 is a mu…

Question

Find the probability that a randomly selected 2-digit number belongs to $\{n\in\mathbb N: 2^n-2	ext{ is a multiple of }3\}$.

Accepted Answer

$2^n-2$ is divisible by 3 for all odd $n$. Two-digit odd numbers: $11,13,\dots,99$, count $=45$, out of 90 total two-digit numbers.

$$P = \frac{45}{90}=\frac12$$

Solutions · 1