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ANSWER
[tex]\text{ P\lparen both students are junior\rparen = }\frac{1}{10}[/tex]EXPLANATION
Given information
The total number of junior students = 2
The total number of senior students = 3
The total number of students = 5
To determine the probability of picking two junior students, follow the steps below
Step 1: Define probability
[tex]\text{ Probability = }\frac{\text{ possible outcome}}{\text{ total outcome}}[/tex]Step 2: Find the probability of picking the first junior students
[tex]\begin{gathered} \text{ Probability = }\frac{possible\text{ outcome}}{total\text{ outcome}} \\ \text{ Probability of picking the first junior students is} \\ \text{ P\lparen Junior student\rparen = }\frac{2}{5} \end{gathered}[/tex]Assuming the first picking was successful, then, we will be left with 1 junior student and 3 senior students.
Therefore, the new total outcome can be calculated below
1 + 3 = 4 students
Step 3: Find the probability that the second picking will be a junior student
[tex]\begin{gathered} \text{ Probability = }\frac{\text{ possible outcome}}{\text{ total outcome}} \\ \text{ P\lparen picking the second junior student\rparen = }\frac{1}{4} \end{gathered}[/tex]Step 4: Find the probability that both students are junior students
[tex]\begin{gathered} \text{ P\lparen both students are junior students\rparen = }\frac{2}{5}\times\frac{1}{4} \\ \text{ P\lparen both students are junior students\rparen = }\frac{2}{20} \\ \text{ P \lparen both students are junior students \rparen = }\frac{1}{10} \end{gathered}[/tex]Hence, the probability that both students selected are juniors is 1/10
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