A vendor at a farmer’s market sells two kinds of mini-cakes: cakes with chocolate icing and cakes with vanilla icing. From past experience, 65% of the customers purchase the cakes with chocolate icing. During the first hour, 18 customers purchased the mini-cakes.

Determine the probability that exactly 12 of the 18 customers chose the chocolate cakes.

Answer:

Given information:

The probability of success $(p)=0.65$

Sample size $(n)=18$

Solution:

→ The probability that exactly 12 of the 18 customers chose the chocolate cakes :

$$\text{P}(x=12)=(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n-x}{|}_{x=12}$$ $$=(\genfrac{}{}{0ex}{}{18}{12})\cdot {0.65}^{12}\cdot (1–0.65{)}^{18-12}$$ $$=0.1941$$