The probability of a defective egg in a lot of 400 eggs is 0.035. Calculate the number of defective eggs in the lot. Also calculate the probability of taking out a non defective egg from the lot.

Answer

To solve the problem, we will break it down into two parts: calculating the number of defective eggs and then calculating the probability of selecting a non-defective egg.

### Step-by-Step Solution:

**Step 1: Calculate the number of defective eggs.**

We are given:
- Total number of eggs = 400
- Probability of a defective egg (P(defective)) = 0.035

To find the number of defective eggs (let's denote it as \( x \)), we can use the formula for probability:

\[ P(\text{defective}) = \frac{\text{Number of defective eggs}}{\text{Total number of eggs}} \]

Substituting the known values into the formula:

\[ 0.035 = \frac{x}{400} \]

Now, we can solve for \( x \):

\[ x = 0.035 \times 400 \]

Calculating this gives:

\[ x = 14 \]

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

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**Step 2: Calculate the probability of taking out a non-defective egg.**

To find the probability of selecting a non-defective egg (let's denote it as \( P(\text{non-defective}) \)), we can use the relationship between the probabilities of complementary events:

\[ P(\text{non-defective}) = 1 - P(\text{defective}) \]

We already know \( P(\text{defective}) = 0.035 \). Therefore:

\[ P(\text{non-defective}) = 1 - 0.035 \]

Calculating this gives:

\[ P(\text{non-defective}) = 0.965 \]

So, the probability of taking out a non-defective egg from the lot is **0.965**.

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### Summary of Results:
- Number of defective eggs: **14**
- Probability of taking out a non-defective egg: **0.965**

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