A programmer noted the results of attempting to run 20 programs. The results showed that 2 programs ran correctly in the first attempt, 7 ran correctly in the second attempt, 5 ran correctly in the third attempt, 4 ran correctly in the fourth attempt and 2 ran correctly in the fifth attempt. What is the probability that his next programme will run correctly on the third run ?

Options

A. `1/4`
B. `1/3`
C. `1/6`
D. `1/5`

Answer

To solve the problem, we need to determine the probability that the next program will run correctly on the third attempt based on the data provided. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify Total Programs
The programmer attempted to run a total of 20 programs.

**Hint:** Always start by identifying the total number of trials or attempts when calculating probabilities.

### Step 2: Identify Successful Outcomes on the Third Attempt
From the data provided, we know that 5 programs ran correctly on the third attempt.

**Hint:** Look for the specific attempt mentioned in the question to find the number of successful outcomes.

### Step 3: Calculate the Probability
The probability of an event is calculated using the formula:

\[ \text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Outcomes}} \]

In this case, the number of successful outcomes on the third attempt is 5, and the total outcomes are 20. Therefore, the probability is:

\[ \text{Probability} = \frac{5}{20} \]

### Step 4: Simplify the Probability
Now, simplify the fraction:

\[ \frac{5}{20} = \frac{1}{4} \]

### Step 5: Conclusion
The probability that the next program will run correctly on the third attempt is \( \frac{1}{4} \).

**Final Answer:** The correct option is \( \frac{1}{4} \).

---