Question

the venn diagram below shows the data collected at a sandwich shop for the last six months with respect to the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich. use this data to answer the following question: what is the probability that a randomly selected person would not choose sourdough or no cheese? without cheese 15% sourdough bread 55% 10% with cheese 20%

Explanation:

Step1: Find probability of sourdough or no - cheese

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event of choosing sourdough bread and $B$ be the event of choosing no - cheese. So $P(A)=(10 + 55)\%=65\%$, $P(B)=(10 + 15)\%=25\%$ and $P(A\cap B)=10\%$. Then $P(A\cup B)=65\%+25\% - 10\%=80\%$.

Step2: Find probability of not choosing sourdough or no - cheese

The probability of the complement of an event $E$ is $P(\overline{E})=1 - P(E)$. So if $E$ is the event of choosing sourdough or no - cheese, then the probability of not choosing sourdough or no - cheese is $P = 1-80\% = 20\%$.

Answer:

20%