a small class has 9 students, 3 of whom are girls and 6 of whom are boys. the teacher is going to choose two…

a small class has 9 students, 3 of whom are girls and 6 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 boy and the second will be a girl? write your answer as a fraction in simplest form.

a small class has 9 students, 3 of whom are girls and 6 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 boy and the second will be a girl? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of first - boy

The probability that the first student chosen is a boy is the number of boys divided by the total number of students. There are 6 boys and 9 students in total, so the probability $P(B_1)=\frac{6}{9}$.

Step2: Calculate probability of second - girl

After choosing a boy first, there are 8 students left and 3 girls. So the probability that the second student chosen is a girl given that the first was a boy is $P(G_2|B_1)=\frac{3}{8}$.

Step3: Calculate joint - probability

By the multiplication rule for dependent events $P(B_1\cap G_2)=P(B_1)\times P(G_2|B_1)$. Substitute the values: $\frac{6}{9}\times\frac{3}{8}=\frac{18}{72}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$