In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that :
(i) it is acceptable to a trader who accepts only a good shirt .
(ii) it is acceptable to a trader who reject only a shirt with major defects ?

Answer

To solve the problem step by step, we will determine the probabilities for both parts of the question.

### Step 1: Understand the total number of shirts and their conditions
- Total shirts = 50
- Good shirts = 44
- Shirts with minor defects = 4
- Shirts with major defects = 2

### Step 2: Calculate the probability for part (i)
**(i) Probability that it is acceptable to a trader who accepts only a good shirt.**

1. **Identify the favorable outcomes:**
- The trader only accepts good shirts.
- Therefore, the number of favorable outcomes (good shirts) = 44.

2. **Identify the total outcomes:**
- The total number of shirts = 50.

3. **Calculate the probability:**
\[ P(\text{Good shirt}) = \frac{\text{Number of good shirts}}{\text{Total number of shirts}} = \frac{44}{50} = \frac{22}{25} \]

### Step 3: Calculate the probability for part (ii)
**(ii) Probability that it is acceptable to a trader who rejects only a shirt with major defects.**

1. **Identify the favorable outcomes:**
- The trader rejects shirts with major defects.
- Therefore, the number of shirts that are acceptable = Total shirts - Major defect shirts = 50 - 2 = 48.

2. **Identify the total outcomes:**
- The total number of shirts = 50.

3. **Calculate the probability:**
\[ P(\text{Acceptable shirt}) = \frac{\text{Number of acceptable shirts}}{\text{Total number of shirts}} = \frac{48}{50} = \frac{24}{25} \]

### Final Results
- The probability that it is acceptable to a trader who accepts only a good shirt is \( \frac{22}{25} \).
- The probability that it is acceptable to a trader who rejects only a shirt with major defects is \( \frac{24}{25} \).

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