Question

Conditional probability please solve. 60 points no wrong answers :)

Answer 1

0.16

Explanation:

The total number of students is 1073.

From inspection of the given two-way table, we can see that the number of students who are graduates and history majors is 73. Therefore:

• P(graduate and history) = 73/1073

The total number of students whose major is history is 463. Therefore:

• P(history) = 463/1073

To find the probability that a student is a graduate, given they are a history major, divide P(graduate and history) by P(history):

`\begin{aligned}\sf P(graduate\:|\:history)&=\sf (P(graduate\;and\;history))/(P(history))\\\\&=\sf ((73)/(1073))/((463)/(1073))\\\\&=(73)/(463)\\\\&=\sf 0.157667386...\\\\&=\sf 0.16\;(nearest\;hundredth)\end{aligned}`

Therefore, the probability that a student is a graduate student, given they are a history major, is 0.16 rounded to the nearest hundredth.