Question

lf In a promotion initiative for a particular chocolate bar a sales person in a su permarket has a 20% chance of selling a bar, to each customer who tries one. If 10 customers try the product what is the probability that 3 or more bars will be sold? Quote the underlying probability distribution. What is the number of customers required to try the chocolate in order to ensure a better than 50% chance of one or more bars being sold? [6

Answer 1

is probability that a bar is sold to a customer who tries it

p = 20% = 0.20

Out of $n=10$ customers who try it, the number of customers who will buy it is a binomial distribution with parameters

$X\sim B\left (n,p \right )$

So that $P(X\geq 3)=1-P(X<3)=1-P(X=0)-P(X=1)-P(X=2)$

Which is $P(X\geq 3)=$$0.3222$ (after rounding to 4 decimal places)

We want to find such that $P(X\geq 1)=1-P(X=0)\geq 0.5$

But $P(X=0)=\binom{n}{0}p^0(1-p)^n=(1-p)^n$

So we want $P(X\geq 1)=1-P(X=0)=1-(1-p)^n\geq 0.5$

That is,

(1-p)n < 0.5 7t (0.8)" < 0.5 7L

$n=4$ is the minimum such integer value and so we must have at least 4 people must try the chocolate in order to ensure a 50% probability of one or more of them buying a chocolate