Question

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 1

Answer: Our required probability is $\dfrac{1}{7}$

Step-by-step explanation:

Since we have given that

P(Junior ) = $\dfrac{1}{2}$

P(Senior) = $\dfrac{1}{2}$

Let the given event be 'C' taking calculus.

P(C|J) = 10% = 0.10

P(C|S) = 60% = 0.60

We need to find the probability that the student is a junior.

So, our required probability is given by

$P(J|C)=\dfrac{P(J).P(C|J)}{P(S).P(C|S)+P(J).P(C|J)}\\\\P(J|C)=\dfrac{0.5\times 0.1}{0.5\times 0.1+0.5\times 0.6}\\\\P(J|C)=\dfrac{0.05}{0.05+0.3}\\\\P(J|C)=\dfrac{0.05}{0.35}\\\\P(J|C)=\dfrac{5}{35}\\\\P(J|C)=\dfrac{1}{7}$

Hence, our required probability is $\dfrac{1}{7}$