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. (the table is presented with rows: m, s, e, h, total; columns: fr, so, total. the values are: m - fr: 78, so: 38, total: 116; s - fr: 32, so: 65, total: 97; e - fr: 59, so: 42, total: 101; h - fr: 43, so: 51, total: 94; total - fr: 212, so: 196, total: 408) which expression represents the conditional probability that a randomly selected freshman has english as the first class of the day? ( p(quad) ) what is the probability that a randomly selected freshman has english as the first class of the day?

Explanation:

Step 1: Identify the relevant counts

We need the number of freshmen (Fr) who have English (E) as their first class and the total number of freshmen. From the two - way table:

• Number of freshmen with English as first class, \(n(\text{Fr and E}) = 59\)
• Total number of freshmen, \(n(\text{Fr})=212\)

Step 2: Calculate the probability

The formula for the probability that a randomly selected freshman has English as the first class is \(P=\frac{\text{Number of freshmen with English}}{\text{Total number of freshmen}}\)

Substitute the values: \(P = \frac{59}{212}\) (If we simplify this fraction, we can divide numerator and denominator by GCD(59,212). Since 59 is a prime number and 59 does not divide 212, the fraction is in simplest form. As a decimal, \(\frac{59}{212}\approx0.278\))

Answer:

The probability is \(\frac{59}{212}\) (or approximately \(0.278\))