To solve the question, let's first understand the given information:
- The jar contains 5 quarters, 2 nickels, and 3 dimes.
- We are drawing one coin, replacing it, and then drawing another coin.
- We need to find the probability of first drawing a quarter and then drawing a nickel.
### Step 1: Calculate the total number of coins
The total number of coins in the jar is the sum of quarters, nickels, and dimes:
[tex]\[ 5 \text{ (quarters)} + 2 \text{ (nickels)} + 3 \text{ (dimes)} = 10 \text{ (total coins)} \][/tex]
### Step 2: Calculate the probability of drawing a quarter
The probability of drawing a quarter on the first draw is given by the ratio of the number of quarters to the total number of coins:
[tex]\[ P(Q) = \frac{5 \text{ (quarters)}}{10 \text{ (total coins)}} = \frac{5}{10} = \frac{1}{2} \][/tex]
### Step 3: Calculate the probability of drawing a nickel
Since we are replacing the coin after the first draw, the total number of coins remains the same. Therefore, the probability of drawing a nickel on the second draw is:
[tex]\[ P(N) = \frac{2 \text{ (nickels)}}{10 \text{ (total coins)}} = \frac{2}{10} = \frac{1}{5} \][/tex]
### Step 4: Calculate the combined probability
To find the probability of drawing a quarter first and then a nickel, we multiply the probabilities of each action:
[tex]\[ P(Q \text{ then } N) = P(Q) \times P(N) = \left( \frac{1}{2} \right) \times \left( \frac{1}{5} \right) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \][/tex]
### Conclusion
The probability of drawing a quarter and then a nickel is:
[tex]\[ \frac{1}{10} \][/tex]
Therefore, the correct choice is:
[tex]\[ \frac{1}{10} \][/tex]
