Question

using a two - way table to find probabilities
at west view high school, every freshman (fr) and sophomore (so)
has either math (m), science (s), english (e), or history (h) as the first
class of the day. the two - way table shows the distribution of students
by first class and grade level.
which expression represents the conditional probability that a
randomly selected freshman has english as the first class of the day?
what is the probability that a randomly selected freshman has english
as the first class of the day?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a two - way table, if we want to find the probability that a student has English (E) given that the student is a freshman (Fr), the formula becomes \(P(E|Fr)=\frac{\text{Number of freshmen with English}}{\text{Total number of freshmen}}\)

Step2: Identify the values from the table

From the table, the number of freshmen with English as the first - class (\(n(E\cap Fr)\)) is \(59\), and the total number of freshmen (\(n(Fr)\)) is \(212\)

Answer:

The expression is \(P(E|Fr)\) and the probability is \(\frac{59}{212}\approx0.278\)