In a class there are 14 boys and 10 girls. If one child is absent, the probability that it is a boy is

Options

A. `(5)/(12)`
B. `(7)/(12)`
C. `(10)/(14)`
D. `(1)/(3)`

Answer

To find the probability that a child who is absent is a boy, we can follow these steps:

### Step 1: Determine the total number of students
We know that there are 14 boys and 10 girls in the class.

Total number of students = Number of boys + Number of girls
Total number of students = 14 + 10 = 24

### Step 2: Identify the number of boys
The number of boys in the class is given as 14.

### Step 3: Calculate the probability of a boy being absent
The probability of an event is calculated using the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case, the favorable outcome is that the absent child is a boy, which is 14 (the number of boys). The total number of outcomes is the total number of students, which is 24.

So, the probability that the absent child is a boy is:
Probability = Number of boys / Total number of students
Probability = 14 / 24

### Step 4: Simplify the fraction
We can simplify the fraction 14/24 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

14 ÷ 2 = 7
24 ÷ 2 = 12

Thus, the simplified probability is:
Probability = 7 / 12

### Final Answer
The probability that the absent child is a boy is **7/12**.

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