Question

The following two-way table describes student's after school activities. Find the probability that a randomly selected student either does sports or works. Grade Sports Music/Drama Work Sophomore 20 7 3 Junior 20 13 Senior 25 5 5 P(Sports U Work) = [? ]% Round to the nearest whole percent. 2​

Answer 1

75%

Step-by-step explanation:

The probability of interest is the ratio of the total of students doing sports or work to the total number of students.

Sports or Work

The column totals are ...

`\begin{tabular}c\cline{1-3}Sports&Drama&Work\\\cline{1-3}65&25&10\\\cline{1-3}\end{tabular}`

Then the number of students doing Sports or Work is 65+10 = 75.

Probability

If a student is picked randomly from those described by the table, the probability of that student doing Sports or Work is the ratio of those choosing those activities to the total number of students.

The total number of students is ...

65 +25 +10 = 100

The ratio of those doing Sports or Work to the total is ...

75/100 = 0.75 = P(sports or work) = 75%