easy Probability
A release-checked easy problem for training Cards, Bayes' Theorem, Conditional Probability.
Suppose you have $n$ red and $n$ blue cards. Each of the $n$ cards of each color have distinct labels $1$ to $n$. $1 \leq k \leq n$ blue cards are removed uniformly at random, and then one card is selected uniformly at random from the remaining $2n-k$ cards. Given that the value is $1$, find the probability the card is blue. Report the answer when $n = 10$ and $k = 4$.
This Probability problem is tagged Cards, Bayes' Theorem, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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