There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

Step 1: Identify Total Number of Outcomes

To calculate probability, we first need to determine the total number of possible outcomes. In this case, the total number of possible outcomes is the total number of students in the class, which is 40. This is because any one of the 40 students can be selected as the class representative.

Step 2: Calculate Probability of Selecting a Girl

Now we need to find the probability of selecting a girl. The number of favorable outcomes for this event is the number of girls, which is 25. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Step 3: Simplify Probability of Selecting a Girl

The fraction representing the probability of selecting a girl can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5. This gives us the simplified probability of $\frac{5}{8}$.

Step 4: Calculate Probability of Selecting a Boy

Next, we find the probability of selecting a boy. The number of favorable outcomes for this event is the number of boys, which is 15. The probability is then calculated by dividing the number of boys by the total number of students.

Step 5: Simplify Probability of Selecting a Boy

Finally, we simplify the fraction representing the probability of selecting a boy. Both the numerator and the denominator can be divided by their greatest common divisor, which is 5. This simplification yields the probability of $\frac{3}{8}$.

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