Question

survey data were gathered on the unlv campus collecting information on the students academic standing and their favorite place in nevada to go for a hike. the raw data were as follows: ( a_{11}=83 ), ( a_{12}=114 ), ( a_{13}=55 ), ( a_{21}=90 ), ( a_{22}=112 ), ( a_{23}=37 ), ( a_{31}=64 ), ( a_{32}=84 ), ( a_{33}=57 ), ( a_{41}=81 ), ( a_{42}=128 ), ( a_{43}=55 ). the above raw data were then used to create the following contingency table. note that you need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. calculate the probability that a unlv students favorite place to hike is red rock, given that the student is a freshman. (for answers up to four decimal places, enter the number in the box below without rounding it. for answers that have more than four decimal values, round your answer to four decimal places).

Explanation:

Step1: Calculate the row total for Freshman

The row total for Freshman is \(83 + 114+55=252\)

Step2: Use the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of contingency tables, if \(A\) is the event that the favorite place is Red - Rock and \(B\) is the event that the student is a Freshman, then \(P(A|B)=\frac{\text{Number of Freshman who like Red Rock}}{\text{Total number of Freshman}}\)

We know that the number of Freshman who like Red Rock \(a_{11} = 83\) and the total number of Freshman (from Step 1) is \(252\)

So \(P=\frac{83}{252}\approx0.3294\)

Answer:

\(0.3294\)