Final answer:
The probability of drawing two even numbers from the stack of cards labeled 5 through 9 is 1/10. The sample space includes the even numbers 6 and 8, and after one even is drawn, there will be only one even left for the second draw.
Step-by-step explanation:
The student is asking about the probability of drawing two even numbers from a stack of cards labeled 5, 6, 7, 8, and 9.
The sample space for drawing an even number first would be {6, 8}. Therefore, the probability of drawing an even number on the first draw is 2 out of 5, or P(First Even) = 2/5. If the first card drawn is even, it is not replaced, so one even card is out of the pool, leaving one even number and three odd numbers in the stack.
For the second draw, the pool of cards is {5, 7, 8, 9} if 6 was drawn, or {5, 6, 7, 9} if 8 was drawn. In either case, there's only one even number left. So, the probability of drawing an even number on the second draw after an even number has already been drawn is 1 out of 4, or P(Second Even | First Even) = 1/4.
Therefore, the probability of drawing two even numbers is the product of the probabilities of each event: P(Two Evens) = P(First Even) × P(Second Even | First Even) = (2/5) × (1/4) = 2/20 or 1/10 after simplification.