We have to find the probability that the chosen student has taken a public speaking class or is majoring in business administration.
To find that we have to divide the number of students that have taken a public speaking class (PS) or majoring in business administration (BA) by the total number of students.
We can find the numerator of this quotient as:
[tex]\begin{gathered} PB\cup BA=PB+BA-(PB\cap BA) \\ PB\cup BA=(10+20)+(10+45)-10 \\ PB\cup BA=10+20+45 \\ PB\cup BA=75 \end{gathered}[/tex]
NOTE: we can calculate the number of elements for a union of two sets by adding the number of elements of each set and substracting the number of elements in the intersection of both sets. This last term is needed to avoid adding these elements twice.
The total number of students is N = 10+20+45+25 = 100, so we can calculate the probability as:
[tex]P(BA\cup PS)=\frac{BA\cup PS}{N}=\frac{75}{100}=0.75[/tex]
Answer: the probability is 0.75.
