Question

A small class has 10 students, 5 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a girl and the second will be a boy? Write your answer as a fraction in simplest form.

Answer 1

Answer:

The required probability is 5/18.

Step-by-step explanation:

Total number of total students = 10

Number of girls = 5

Number of boys = 5

Formula for probability:

$Probability=\frac{\text{Favorable outcome}}{\text{Total outcome}}$

The probability that the first student chosen will be a girl = $\frac{5}{10}=\frac{1}{2}$

After selecting 1 student, the total number of student is

$10-1=9$

The probability that the second student chosen will be a boy = $\frac{5}{9}$

The probability that the first student chosen will be a girl and the second will be a boy is

$P=\frac{1}{2}\times \frac{5}{9}$

$P=\frac{5}{18}$

Therefore the required probability is 5/18.

Answer 2

5 girls, 5 boys...total of 10 students

P(1st pick is a girl) = 5/10 which reduces to 1/2
P(2nd pick is a boy) = 5/9 

P (both) = 1/2 * 5/9 = 5/18 <=