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

ANSWER

$P(PS\cup BA)=\frac{3}{4}$

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:

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

Therefore:

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

That is the answer.