>>125967831. 2/3
P(A|B) = P(A & B)/P(B)
P(A) is the probability of picking a blue ball in your second selection
P(B) is the probability of picking a blue ball in your first selection
P(A & B) = 1/3, because you pick the two balls from the same box and if you pick from box 1 then you will 100% get 2 blue balls, and if you pick from any other box you will 0% get 2 blue balls, and there is an equal chance of picking from any box, so 1/3 * 1 + 1/3 * 0 + 1/3 * 0 = 1/3.
P(B) = 1/2, because: 100% chance if you pick from box 1, 50% chance if you pick from box 2, 0% chance if you pick from box 3, equal chance of picking from each box, so 1/3 * 1 + 1/3 * 1/2 + 1/3 * 0 = 1/2.
P(A|B) = P(A & B)/P(B) = (1/3) / (1/2) = 2/3
2. 1/2
P(A|B) = P(A & B)/P(B)
P(A) and P(B) represent the same probabilities as in part 1, however the restriction of the balls being from the same box is lifted
P(A & B) = 4/7 * 3/6 = 2/7
P(B) = 4/7
P(A|B) = P(A & B)/P(B) = (2/7) / (4/7) = 1/2
3. Question 3 is equivalent to question 2, as none of the conditions are changing, so 1/2.
