Die, roulette wheel and card all showing the same number

Question

In a casino you roll a fair six-sided die, spin an American roulette wheel (38 equally likely pockets: $0$ , $00$ and $1$ to $36$ ), and draw one card from a standard 52-card deck, counting an ace as $1$ . What is the probability that all three show the same number?

Short answer

$\tfrac{1}{494}$ . Whatever the die shows, $d\in\{1,\dots,6\}$ , the card has rank $d$ with probability $\tfrac4{52}=\tfrac1{13}$ and the wheel lands on $d$ with probability $\tfrac1{38}$ . By independence the answer is $\tfrac{1}{13\cdot38}=\tfrac1{494}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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