Out of 132 screws in a pack, 12 screws are known to be defective. If one screw is picked up at random, the probability that it is a good screw is

Options

A. `1//11`
B. `10//11`
C. `2//3`
D. `9//10`

Answer

To find the probability that a randomly picked screw from a pack of 132 screws is a good screw, we can follow these steps:

### Step 1: Identify the total number of screws and the number of defective screws.
- Total screws in the pack = 132
- Defective screws = 12

### Step 2: Calculate the number of good screws.
- Good screws = Total screws - Defective screws
- Good screws = 132 - 12 = 120

### Step 3: Understand the concept of probability.
- Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes.

### Step 4: Determine the favorable outcomes.
- In this case, the favorable outcome is picking a good screw. The number of good screws is 120.

### Step 5: Calculate the probability of picking a good screw.
- Probability (P) of picking a good screw = (Number of good screws) / (Total number of screws)
- P = 120 / 132

### Step 6: Simplify the fraction.
- To simplify 120 / 132, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 12.
- 120 ÷ 12 = 10
- 132 ÷ 12 = 11
- Therefore, P = 10 / 11

### Final Answer:
- The probability that a randomly picked screw is a good screw is **10/11**.

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