Suppose that a magnet high school includes grades 11 and 12, with half of the students in each grade. 60% of the senior class and 10% of the junior class are taking calculus. Suppose a calculus student is randomly selected to accompany the math teachers to a conference. What is the probability that the student is a junior? (Enter your answer as a fraction.)

Answer: Our required probability is [tex]\dfrac{1}{7}[/tex]Step-by-step explanation:Since we have given that P(Junior ) = [tex]\dfrac{1}{2}[/tex]P(Senior) = [tex]\dfrac{1}{2}[/tex]Let the given event be 'C' taking calculus.P(C|J) = 10% = 0.10P(C|S) = 60% = 0.60We need to find the probability that the student is a junior.So, our required probability is given by[tex]P(J|C)=\dfrac{P(J).P(C|J)}{P(S).P(C|S)+P(J).P(C|J)}\\\\P(J|C)=\dfrac{0.5\times 0.1}{0.5\times 0.1+0.5\times 0.6}\\\\P(J|C)=\dfrac{0.05}{0.05+0.3}\\\\P(J|C)=\dfrac{0.05}{0.35}\\\\P(J|C)=\dfrac{5}{35}\\\\P(J|C)=\dfrac{1}{7}[/tex]Hence, our required probability is [tex]\dfrac{1}{7}[/tex]