Final answer:
The probability of drawing a dime and then another dime from the jar without replacement is 2/9.
Step-by-step explanation:
The question is asking to calculate the probability of drawing two dimes one after the other from a jar that contains 3 quarters, 5 dimes, and 2 nickels, without replacing the first dime before drawing the second. To solve this, we use the concept of conditional probability.
First, we find the probability of drawing a dime. There are 10 coins in total (3+5+2), so the probability of drawing a dime on the first draw is 5/10 or 1/2.
Assuming we have taken one dime out, there are now 9 coins left and 4 of them are dimes. Therefore, the probability of drawing a dime on the second draw is 4/9.
We then multiply these probabilities together to get the overall probability of drawing a dime and then another dime: (1/2) × (4/9), which equals 4/18 or 2/9 when simplified.