The probability of getting a bad egg from a lot of 400 eggs is 0.035. Find the number of bad eggs in the lot. Also find the probability of getting a good egg.

Options

A. 7,0.965
B. 14,0.965
C. 14,0.65
D. 7,0.65

Answer

To solve the problem step by step, we will first find the number of bad eggs in the lot and then calculate the probability of getting a good egg.

### Step 1: Determine the number of bad eggs
We know the probability of getting a bad egg from a lot of 400 eggs is given as 0.035.

The formula for probability is:
\[ P(\text{Bad Egg}) = \frac{\text{Number of Bad Eggs}}{\text{Total Number of Eggs}} \]

Let \( x \) be the number of bad eggs. Therefore, we can write:
\[ 0.035 = \frac{x}{400} \]

To find \( x \), we can rearrange the equation:
\[ x = 400 \times 0.035 \]

Now, calculate \( x \):
\[ x = 400 \times 0.035 = 14 \]

So, the number of bad eggs in the lot is **14**.

### Step 2: Determine the number of good eggs
The total number of eggs is 400. To find the number of good eggs, we subtract the number of bad eggs from the total:
\[ \text{Number of Good Eggs} = \text{Total Number of Eggs} - \text{Number of Bad Eggs} \]
\[ \text{Number of Good Eggs} = 400 - 14 = 386 \]

### Step 3: Calculate the probability of getting a good egg
Now, we can find the probability of getting a good egg using the same probability formula:
\[ P(\text{Good Egg}) = \frac{\text{Number of Good Eggs}}{\text{Total Number of Eggs}} \]
\[ P(\text{Good Egg}) = \frac{386}{400} \]

Now, simplify this fraction:
\[ P(\text{Good Egg}) = 0.965 \]

### Final Answers:
- The number of bad eggs in the lot is **14**.
- The probability of getting a good egg is **0.965**.