Question

A survey of 100 high school students provided thisfrequency table on how students get to school:Drive toTake theGradeWalkSchoolbusSophomore2253Junior13202Senior2555Find the probability that a randomly selected studenteither takes the bus or walks.[?P(Take the bus U Walk)

Answer 1

Let's call the event of a student taking the bus as event A, and the event of a student walking as event B. The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have a total of 100 students, where 50 of them take the bus and 10 of them walk. This gives to us the following informations:

`\begin{gathered} P(A)=(50)/(100) \\ P(B)=(10)/(100) \end{gathered}`

The additive property of probability tells us that:

`P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B)`

Since our events are mutually exclusive(the student either walks or takes the bus), we have:

`P(A\:and\:B)=0`

Then, our probability is:

`P(A\cup B)=(50)/(100)+(10)/(100)-0=(60)/(100)=(3)/(5)`

The answer is:

`P(Take\:the\:bus\cup Walk)=(3)/(5)`