Question

What is the probability that a patron had a sandwich but did not order soup

Answer 1

`\begin{gathered} P(A)=Probability\text{ the patron has soup } \\ P(A)=(50)/(95)=(10)/(19) \\ P(B)=Probability\text{ the patron has sandwich } \\ P(B)=(60)/(95)=(12)/(19) \\ P(A\cup B)=Probability\text{ the patron has soup or sandwich} \\ P(A\cup B)=? \\ P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cap B)=Probability\text{ the patron has soup and sandwich} \\ P(A\cap B)=(30)/(95)=(6)/(19) \\ P(A\cup B)=(10)/(19)+(12)/(19)-(6)/(19) \\ P(A\cup B)=(16)/(19)=0.8421=84.21\text{\%} \\ \text{The }Probability\text{ the patron has soup or sandwich is }84.21\text{\%} \end{gathered}`