Question

A class consists of 12 boys and 18 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.
(a) 0.4
(b) 0.5
(c) 0.7
(d) None of these

Answer 1

Hint: Add the number of boys and number brown eyed girls to get the number of favourable outcomes. The total outcomes for the above question is 12+18=30. Finally use the formula $\text{Probability}=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ to get the answer. For finding the number of brown eyed girls use the statement that half of the girls have brown eyes.

Complete step-by-step answer:
Probability in simple words is the possibility of an event to occur.
Probability can be mathematically defined as $=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ .
Now, let’s move to the solution to the above question. It is given that there are 12 boys and 18 girls, out of which half of the girls and half of the boys have brown eyes. So, the number of girls with brown eyes is half of 18, i.e., 9. So, the total number of favourable outcomes is the number of boys added with the number of girls having brown eyes. So, the total favourable outcome is 12+9=21.
The total number of outcomes is equal to the total number of students, 18+12=30.
 $\text{Probability}=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}=\dfrac{21}{30}=\dfrac{7}{10}=0.7$
Therefore, the answer to the above question is option (c).



Note:If you want you can find the favourable outcomes by adding the number of boys with total number of brown eyed students as well, but don’t forget to subtract the overlapping cases, i.e., considering the possibility that there can be boys who are having brown eyes at the same time.