Question

Sara is reviewing recent orders at her deli to determine which meats she should order. She found that of 1,000 orders, 390 customers ordered turkey, 345 customers ordered ham, and 300 customers ordered neither turkey nor ham. Based on these data, how many of the next 1,000 customers will order both turkey and ham? Show your work and use complete sentences.

Answer 1

We can make use of the following equation for combined events:
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]
where A and B are two events whose union ( being the event A or B or both) is the probability of A plus the probability of B minus the intersection of A and B.
In your question, the union of turkey and ham is:
Total number of orders - number of orders with no turkey or ham
-------------------------------------------------------
Total number of orders
So we get:
\[P(T\cup H)=\frac{1000-300}{1000}=\frac{700}{1000}\]
and
\[\frac{700}{1000}=\frac{390}{1000}+\frac{345}{1000}-P(T\cap H)\]
Therefore the probability a customer will order both turkey and ham is:
\[P(T\cap H)=\frac{735}{1000}-\frac{700}{1000}=\frac{35}{1000}\]
So the expected number of customers out of the next 1000 customers who will order both turkey and ham is 35 customers.