at west view high school, every freshman (fr) and sophomore (so) has either math (m), science (s), english…

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.\nwhich expression represents the conditional probability that a randomly selected freshman has english as the first class of the day?\nwhat is the probability that a randomly selected freshman has english as the first class of the day?\n| | m | s | e | h | total |\n|----|----|----|----|----|----|\n| fr | 78 | 32 | 59 | 43 | 212 |\n| so | 38 | 65 | 42 | 51 | 196 |\n| total | 116 | 97 | 101 | 94 | 408 |

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.\nwhich expression represents the conditional probability that a randomly selected freshman has english as the first class of the day?\nwhat is the probability that a randomly selected freshman has english as the first class of the day?\n| | m | s | e | h | total |\n|----|----|----|----|----|----|\n| fr | 78 | 32 | 59 | 43 | 212 |\n| so | 38 | 65 | 42 | 51 | 196 |\n| total | 116 | 97 | 101 | 94 | 408 |

Answer

Answer:

  1. $P(E|Fr)$
  2. $\frac{59}{212}$

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the problem, we want to find the probability that a student has English as the first - class given that the student is a freshman. So the expression for the conditional probability is $P(E|Fr)$.

Step2: Calculate the probability

The number of freshmen with English as the first class is 59, and the total number of freshmen is 212. So the probability that a randomly selected freshman has English as the first class of the day is $\frac{\text{Number of freshmen with English}}{\text{Total number of freshmen}}=\frac{59}{212}$.