Final answer:
The probability that the second marble is blue if the first marble is white is approximately 0.58, calculated using the formula for conditional probability P(B|W) = P(W & B) / P(W).
Step-by-step explanation:
The student is asking about the calculation of conditional probability in the context of drawing marbles from a bag. To calculate the probability of drawing a blue marble second, given that a white marble was drawn first, we use the provided probabilities. We know the joint probability of drawing a white marble first and a blue marble second P(W & B) is 0.19 and the probability of drawing a white marble on the first draw P(W) is 0.33.
We apply the formula for conditional probability, which is P(B|W) = P(W & B) / P(W). Plugging in the known values gives us P(B|W) = 0.19 / 0.33. When we divide 0.19 by 0.33, we get approximately 0.58. Therefore, the probability of drawing a blue marble second, given that a white marble has already been drawn, is 0.58 to the nearest hundredth.