Question

At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 48 22 Cold 8 12 on What is the probability that a customer ordered a cold drink given that he or she ordered a large? Rounded to the nearest percent, [? ]%

Answer 1

From the table the probability of large is given by:

$P(L)=\frac{27}{100}$

The probability of cold drink is given from the table as:

$P(C)=\frac{25}{100}$

The probability of a cold large drink is given from table as:

$P(C\cap L)=\frac{5}{100}$

Hence the probability that a customer ordered a cold drink given that the drink was a large is given by:

$\begin{gathered} P(C|L)=\frac{P(C\cap L)}{P(L)} \\ P(C|L)=\frac{\frac{5}{100}}{\frac{27}{100}} \\ P(C|L)=\frac{5}{27}=0.1851851852 \end{gathered}$

Hence the probability is 18.52%.