To find the probability that the sum of two coins picked randomly by Kevin is at least 30 cents, we need to follow a structured approach. Let's break it down into clear steps.
### Step 1: Define Coin Values
Kevin has dimes (10 cents), nickels (5 cents), and quarters (25 cents). We'll represent these as:
- Dime = 10 cents
- Nickel = 5 cents
- Quarter = 25 cents
### Step 2: Determine the Sums of Two Coins
Next, we compute all possible sums when picking two coins:
1. Dime + Dime = 10 + 10 = 20 cents
2. Dime + Nickel = 10 + 5 = 15 cents
3. Dime + Quarter = 10 + 25 = 35 cents
4. Nickel + Nickel = 5 + 5 = 10 cents
5. Nickel + Quarter = 5 + 25 = 30 cents
6. Quarter + Quarter = 25 + 25 = 50 cents
### Step 3: Identify Successful Outcomes
We are interested in outcomes where the sum of the two coins is at least 30 cents. From the list of sums:
- 35 cents (Dime + Quarter)
- 30 cents (Nickel + Quarter)
- 50 cents (Quarter + Quarter)
Out of the six possible sums, three of them are at least 30 cents.
### Step 4: Calculate the Probability
There are a total of 6 possible outcomes when Kevin picks two coins. The number of successful outcomes is 3. Probability is determined as follows:
[tex]\[
\text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{3}{6} = \frac{1}{2}
\][/tex]
### Step 5: Match the Result with Given Options
The probability that the sum of the two coins picked is at least 30 cents is [tex]\(\frac{1}{2}\)[/tex]. This does not seem to match any of the provided options. Re-examining the steps:
- There are six combinations.
- Three outcomes meet the criteria of being at least 30 cents.
- The calculation of the fraction simplifies to [tex]\(\frac{3}{6} = \frac{1}{2}\)[/tex] or 0.5, which does indeed confirm our solution.
Since the final probability is not listed among the given options, there seems to be an inconsistency with the provided options.
After carefully re-evaluating the steps:
None of the given options exactly match our calculated answer of [tex]\(\frac{1}{2}\)[/tex] (0.5). However, given the discrepancy observed, and for educational purposes, a misalignment between calculation and provided options might be possible.
To conclude, whether discussing our calculated answer or any oversight in provided choices:
Thus, the correct probability is [tex]\(\frac{1}{2}\)[/tex].
Lastly, it's crucial to confirm in provided options before concluding, given real-world inaccuracies.
