A science class has 7 girls and 1 boy in the seventh grade and 3 girls and 9 boys in the eighth grade. The teacher randomly selects a seventh and an eighth-grader from the class for a competition. What is the probability that the students she selects are both girls?Write your answer as a fraction in the simplest form.

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Answer:

7/32

Explanation:

The seventh-grade class has 7 girls and 1 boy.

[tex]P(\text{selecting a girl from seventh grade)}=\frac{7}{7+1}=\frac{7}{8}[/tex]

The eighth-grade class has 3 girls and 9 boys.

[tex]P(\text{selecting a girl from eighth grade)}=\frac{3}{3+9}=\frac{3}{12}[/tex]

Therefore, the probability that the students she selects are both girls:

[tex]P(\text{both are girls)}=\frac{7}{8}\times\frac{3}{12}=\frac{7}{32}[/tex]

The probability is 7/32.

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