Probability of getting same number What is the probability of getting the same number when spinning a roulette wheel, tossing a die, and drawing a random card?
My approach:
Case A - Get a random number on the roulette wheel, now get the same number on the die and the card: $$1 \cdot \frac{1}{6} \cdot \frac{1}{13} = \frac{1}{78}$$
Case B - Get a random number on the die, then get the same number on the roulette wheel and the card: $$1 \cdot \frac{1}{6} \cdot \frac{1}{13} = \frac{1}{78}$$
Case C - Get a random number on the card, now get the same number on the  die and the roulette wheel: $$\frac{6}{13} \cdot \frac{1}{6} \cdot \frac{1}{6} = \frac{1}{78}$$ ($\frac{6}{13}$ for the card since we can only choose the numbers $1$–$6$)
Sum all $3$ cases: $$\frac{3}{78} = \bf{\frac{1}{26}}$$
Does this seem right or I am on the wrong approach here?

Assuming it is a US roulette wheel, there are 38 numbers, the die has the most restrictive ($\{1,...,6\}$) and the cards have 52 possibilities.
The total number of selections is $38 \cdot 6 \cdot 52$ and the number of selections that match is $4 \cdot 6$ so the probability is ${1 \over 13 \cdot 38}$ (about $0.2 \%$).
