240 students reside in a hostel. Out of which 50% go for the yoga classes early in the morning, 25% go for the Gym club and 15% of them go for the morning walk. Rest of the students have joined the laughing club. What is the probability of students who have joined laughing club?

Answer

To find the probability of students who have joined the laughing club, we will follow these steps:

### Step 1: Determine the total number of students
The total number of students residing in the hostel is given as 240.

### Step 2: Calculate the number of students attending each activity
1. **Yoga Classes**: 50% of students go for yoga.
\[ \text{Number of students in yoga} = 50\% \text{ of } 240 = \frac{50}{100} \times 240 = 120 \]

2. **Gym Club**: 25% of students go to the gym.
\[ \text{Number of students in gym} = 25\% \text{ of } 240 = \frac{25}{100} \times 240 = 60 \]

3. **Morning Walk**: 15% of students go for a morning walk.
\[ \text{Number of students in morning walk} = 15\% \text{ of } 240 = \frac{15}{100} \times 240 = 36 \]

### Step 3: Calculate the total number of students involved in yoga, gym, and morning walk
Now, we will sum the number of students involved in these activities:
\[ \text{Total students in yoga, gym, and morning walk} = 120 + 60 + 36 = 216 \]

### Step 4: Calculate the number of students in the laughing club
To find the number of students who have joined the laughing club, we subtract the total number of students involved in the other activities from the total number of students:
\[ \text{Number of students in laughing club} = 240 - 216 = 24 \]

### Step 5: Calculate the probability of students in the laughing club
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes is the number of students in the laughing club (24), and the total number of outcomes is the total number of students (240):
\[ \text{Probability of students in laughing club} = \frac{24}{240} = \frac{1}{10} \]

### Final Answer
The probability of students who have joined the laughing club is \(\frac{1}{10}\).

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