easy Probability
A release-checked easy problem for training Law of Total Probability, Combinations and Permutations, Conditional Probability.
You have two bins in front of you, say $1$ and $2$. Bin $i$ has $r_i$ red and $b_i$ blue marbles inside. $1$ marble uniformly at random is selected from bin $1$ and is transferred to bin $2$. Afterwards, a marble is selected uniformly at random from bin $2$. Find the probability that the marble drawn is blue when $r_1 = 4, b_1 = 3, r_2 = 5,$ and $b_2 = 3$.
This Probability problem is tagged Law of Total Probability, Combinations and Permutations, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
Probability · Akuna
Probability
Probability
Probability · SIG, DE Shaw
Probability · SIG, Jane Street
Probability · Jane Street