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-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) รท (Total number of equally likely outcomes). Here each card is equally likely to be drawn.
1. Identify total number of outcomes:\
The teacher has written the names of all 40 students on separate cards. Hence the total number of equally likely outcomes is \( n(S) = 40 \).
2. (i) Probability of drawing a girl:\
- Number of favourable outcomes (girls) = \( n(G) = 25 \).
- Using the definition of probability,\
$$ P(\text{girl}) = \frac{n(G)}{n(S)} = \frac{25}{40} = \frac{5}{8}. $$
3. (ii) Probability of drawing a boy:\
- Number of favourable outcomes (boys) = \( n(B) = 15 \).
- Hence,\
$$ P(\text{boy}) = \frac{n(B)}{n(S)} = \frac{15}{40} = \frac{3}{8}. $$
4. Check: Since the events "girl" and "boy" are complementary,\
$$ P(\text{girl}) + P(\text{boy}) = \frac{5}{8} + \frac{3}{8} = 1, $$
confirming the calculations are correct.
Correct Answer: (i) \(\displaystyle \frac{5}{8}\) (ii) \(\displaystyle \frac{3}{8}\)