Calculate Probability of Third Card Being an Ace
CitadelData Scientist · Technical Screen
Last updated
Evaluates conditional probability with cards drawn without replacement after observing at least one Ace. Strong answers define the conditioning event, account for the number of Aces among the first two cards, and compute the probability that the third card is an Ace as 49/825.
Scenario
A probability puzzle during a first-round technical screen.
Question
You draw three cards without replacement from a standard 52-card deck. Given that among the first two cards there is at least one Ace, what is the probability that the third card is an Ace?
Hints
Condition on the Ace count in the first two draws and apply Bayes.
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