Final answer:
The probability of drawing an even card followed by another even card without replacement from cards labeled 4, 5, 6, 7 is 1/6.
Step-by-step explanation:
To determine the probability of choosing an even-numbered card, followed by another even-numbered card without replacement, given that there are cards labeled 4, 5, 6, 7, we first have to count the number of even cards which are 4 and 6.
When the first card is drawn, the probability of it being even is 2/4 (since there are two even cards out of four total cards). After drawing an even card, there are three cards left, and only one of them is even. So the probability of then drawing another even card is 1/3.
To find the overall probability of both events happening, we multiply the individual probabilities:
P(first even AND second even) = P(first even) × P(second even given first even) = (2/4) × (1/3) = 1/6.