Question

the frequency table (table of counts) below shows the survey data on a group of randomly selected community college students. the students were surveyed about their major study area and their level of expertise in technical writing: $a_{11}=103$, $a_{12}=108$, $a_{13}=46$, $a_{14}=64$, $a_{21}=82$, $a_{22}=160$, $a_{23}=30$, $a_{24}=83$, $a_{31}=267$, $a_{32}=127$, $a_{33}=101$, $a_{34}=212$, $a_{41}=96$, $a_{42}=159$, $a_{43}=49$, $a_{44}=136$ the following contingency table was created based on the above data, where you may need to calculate the total for each row, the total for each column, or the grand total on your own before answering the question that appears after the table. calculate the probability that a student is majoring in humanities, given that the student has intermediate level ability in technical writing. (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 total number of students with intermediate - level ability

Add up the values in the "Intermediate" column:
$$46 + 30+101 + 49=226$$

Step2: Identify the number of students majoring in humanities with intermediate - level ability

From the table, the value for humanities and intermediate is \(a_{33}=101\)

Step3: 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 a contingency table, if \(A\) is "majoring in humanities" and \(B\) is "having intermediate - level ability", then \(P(A|B)=\frac{\text{Number of students in humanities and intermediate}}{\text{Total number of students with intermediate - level ability}}\)
So, \(P=\frac{101}{226}\approx0.4469\)

Answer:

\(0.4469\)