Question

One of these 100 students is selected at random to give more detailed answers to some follow-up questions. What is the probability that the chosen student has taken a public speaking class or is majoring in business administration? Write your answer as a decimal.

Answer 1

`P(PS\cup BA)=(3)/(4)`

Step-by-step explanation

We want to find the probability that the chosen student has taken a public speaking class or is majoring in business administration.

To do this, we have:

`P(PS\cup BA)=P(PS)+P(BA)-P(PS\cap BA)`

That is to find the probability, subtract the probability that the student has taken a public speaking class and is majoring in Business administration from the sum of the probabilities of both.

We have that:

`\begin{gathered} P(PS)=(30)/(100)=(3)/(10) \\ P(BA)=(55)/(100)=(11)/(20) \\ P(PS\cap BA)=(10)/(100)=(1)/(10) \end{gathered}`

Therefore:

`\begin{gathered} P(PS\cup BA)=(3)/(10)+(11)/(20)-(1)/(10) \\ P(PS\cup BA)=(3)/(4) \end{gathered}`

That is the answer.