2 A local shop found based on past observations that 20 of t

2. A local shop found, based on past observations, that 20% of the people who enter the shop will actually buy something. Three potential customers enter the shop. (a) Calculate the probability that least two customers will buy something. (b) What did your calculations in (a) assume? Describe a situation when those assumptions are unrealistic. 3. A company decided to market two new products. After an analysis of the current market conditions and the firm?s past experience, the company believes that the probability that the first product will be successful is 0.6. If the first product is successful, the company believes that the probability that the second product will be successful is 0.4, while, if the first product is not successful, the probability that the second product will be successful is 0.5. Let consider a random variable X = the number of successful products the company will market. (a) What is the pmf/pdf of X?

Solution

(a)Given X follows Binomial distribution with n=3 and p=0.2

P(X=x)=3Cx*(0.2^x)*(0.8^(3-x)) for x=0,1,2,3

So the probability is

P(X>=2) = P(X=2)+P(X=3)

=3C2*(0.2^2)*(0.8^(3-2))+3C3*(0.2^3)*(0.8^(3-3))

=0.104

----------------------------------------------------------------------------------------------------------------------------------

(b) Assume:

The probability that people who enter the shop will buy something is not every time 0.2