Final answer:
The conditional probability of drawing a second white marble given that the first marble drawn is white, with a total of 5 marbles initially, 3 white and 2 black, is ½ or 0.5 since there are now only 2 white and 2 black marbles left in the box.
Step-by-step explanation:
The question involves calculating a conditional probability, which is the probability of an event occurring given that another event has already occurred. Specifically, the question asks for the probability of drawing 2 white marbles from a box that contains 5 marbles, 3 white and 2 black ones, provided that the first marble already drawn is white.
To find the probability of drawing the second white marble given that the first is white, we must adjust the sample space because the first draw has already changed the composition of the marbles in the box. Since the first marble drawn is white, we are left with 2 white and 2 black marbles. The probability of now drawing a white marble is the number of white marbles left (2) divided by the total remaining marbles (4), which equals ½ or 0.5.
Mathematically, the probability is:
P(Second White | First White) = Number of White Marbles Remaining / Total Remaining Marbles
P(Second White | First White) = 2 / 4 = ½ or 0.5