 Hello and welcome to the session. Let's work out the following problem It says if the probability that an individual suffers from reaction by an injection is one upon Thousand find the probability that out of five thousand individuals given that injection Exactly five will suffer No one will suffer from the reaction given that e to the power minus five is equal to 0.00672 Let's now move on to the solution Now we are given that the probability that an individual suffers from injection is one by a thousand so let P be the probability that individual suffers from reaction so P here is one upon 1,000 and we have to find the probability that out of five thousand individuals Exactly five will suffer. So here n is the number of individuals as 5,000 now since n is very large so it forms the poison distribution Where mean m is given by n into p right now n is 5,000 p is 1,000 one upon 1,000 that is equal to five now this is a Poison distribution So this is given by probability of x Equal to r is given by m to the power r into e to the power minus m upon r factorial where r goes from zero one two to infinity Now in the first part we have to find the probability that exactly five will suffer from the reaction So we have to find the probability where x is equal to five now m is five so it is five to the power five Into e to the power minus five upon five factorial now five to the power five is 3,125 into e to the power minus five and it is given to be 0.00672 upon five factorial Five factorial is five into four into three into two into one This is 3,125 into 0.00672 upon 120 3,125 into 0.00672 is 21 upon 120 and this is equal to 0.175 Now in the second part we have to find the probability No one will suffer so we have to find the probability for x is equal to zero so it is m to the power r that is zero into e to the power minus m That is e to the power minus five upon zero factorial so this is Five to the power zero is one into e to the power minus five zero factorial is one So this is e to the power minus five, which is equal to 0.00672 So The probability that exactly five will suffer is 0.175 and the probability that no one will suffer is 0.00672 So this completes the question you must remember that Whenever you have n which is very large you use the Poisson distribution which is given by this So this completes the question and the session why for now take care have a good day