Question

150 students were surveyed on how many text messages to send in a date for different devices. let X represent the number of students using each type of device, cell phone, Chromebook, or other. a. write an equation to represent the number of students who send text messages b. solve for x c. what is the probability that a random choosen student uses their cell phone to send text messages

Answer 1

Given that the total number of students that sent messages = 150 students

a) To obtain the equation to represent the number of students who send text messages, we will sum up the variables in the Venn diagram and equate it to 150.

`\begin{gathered} 75+x+3x+x=150 \\ x+3x+x=150-75 \\ 5x=75 \end{gathered}`

Hence, the equation is

`5x=75`

b) Solving for x

`\begin{gathered} 5x=75 \\ x=(75)/(5)=15 \\ \therefore x=15 \end{gathered}`

Therefore, x = 15.

c) The total number of student that uses cell phone = 75 + x = 75 + 15= 90students

The total number of students that sent messages = 150students

The formula for probability is,

`\text{Probability = }\frac{\text{Number of students that uses cell phone}}{\text{Total number of students}}`

Hence,

`P(\text{Number of students that uses cell phone)}=(90)/(150)=(3)/(5)`

Therefore, the probability that a randomly chosen student uses their cell phone to send text messages ​is 3/5.