The probability that bulbs selected randomly from the lot has life less than 900 h, is

Options

A. `11/40`
B. `5/16`
C. `7/16`
D. `9/16`

Explanation

To solve the problem of finding the probability that bulbs selected randomly from the lot have a life of less than 900 hours, we can follow these steps:

### Step 1: Understand the problem
We need to find the probability of selecting bulbs with a lifetime of less than 900 hours from a total of 80 bulbs.

### Step 2: Gather the data
From the frequency table provided in the problem, we need to identify how many bulbs have a lifetime of less than 900 hours.

### Step 3: Count the favorable outcomes
According to the video transcript, the number of bulbs with a lifetime less than 900 hours is:
- 23 bulbs with a lifetime of 800 hours
- 12 bulbs with a lifetime of 700 hours
- 10 bulbs with a lifetime of 600 hours

Adding these together gives:
\[ 23 + 12 + 10 = 45 \]
So, there are 45 favorable outcomes (bulbs with a lifetime less than 900 hours).

### Step 4: Identify the total number of outcomes
The total number of bulbs in the lot is given as 80.

### Step 5: Calculate the probability
The probability \( P \) of selecting a bulb with a lifetime of less than 900 hours is calculated using the formula:
\[ P(\text{life} < 900) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we have:
\[ P(\text{life} < 900) = \frac{45}{80} \]

### Step 6: Simplify the fraction
To simplify \( \frac{45}{80} \):
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[ \frac{45 \div 5}{80 \div 5} = \frac{9}{16} \]

### Final Answer
Thus, the probability that a randomly selected bulb has a life of less than 900 hours is:
\[ \frac{9}{16} \]

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