Poisson Distributions

Question

Customers arrive at a shop according to a Poisson process at rate λ (/min), where they choose to buy either product A (with probability P) or product B (with probability 1 – P), independently. Given that during the first hour 5 customers chose product B, what is the probability that all the customers that arrive at the shop within the first 10 minutes, all bought product A?

1.   60%
2.  ​​​​​​​ 70%
3.  ​​​​​​​ 30%
4.  ​​​​​​​ 40%

Comments

Rate at which customers buy product B in 10 min = 5*10/60 = 0.84(approx)

Let we are finding pmf for 0 number of products B purchased in 10 min = e-0.84 = 0.4317 ~ 0.40

Hence, 40% probability.

Answer 1

please Verify the answer :

To find probability that all customers buy A in first 10 minutes

i am finding

Probabilty of 0 customer in first 10 minutes to buy B

poissons :

k=0,  t=10min , answer is coming approx to 40%,

if anyone is having proper explanation please upload it

Comments

answer is 40 ..how did you calculate