 Hi and how are you all today? The question says in a book of 200 pages, 200 misprints are randomly distributed. Using poison distribution, calculate the probability that a randomly observed page of a book will be found to have at least 3 errors. Now let P be the probability of selecting a page out of 200 pages. So therefore probability of selecting a page out of 200 pages is 1 upon 200, right? That is equal to 0.005. Now here we are given n that is the total number of misprints as 200. Therefore average number of misprints in the page will be equal to n into P that is 200 into 0.005 that is further equal to 1. Now let x denote the number of misprints in a page. Then x follows poison distribution such that P x equal to r is equal to m raised to the power r e raised to the power minus m divided by r factorial. And we have r as 0, 1, 2, 3 and so on. So we have it equal to 1 raised to the power r e raised to the power minus m upon where again we can write that r is 0, 1, 2, 3 and so on. Now the required probability that is at least 3 errors will be equal to P when x is greater than equal to 3, right? And that will be 1 minus probability that x is less than. So we have equal to 1 minus probability that x is equal to 0 plus probability that x is equal to 1 plus probability that x is equal to 2, right? So we have 1 minus 1 raised to the power 0 e raised to the power minus 1 upon 1 factorial plus 1 raised to the power 1, e raised to the power minus 1 upon 1 factorial. So here it is 0 factorial plus 1 raised to the power 2 e raised to the power minus 1 upon 2 factorial. What we need to do ahead is, we just need to solve it out, we are left with in the bracket e raised to the power minus 1 plus e raised to the power minus 1 plus e raised to the power minus 1 upon 2 factorial can be written as 2 into 1 which is further equal to 1 minus taking e raised to the power minus 1 common out we are left with 1 plus 1 plus 1 by 2 that is 1 minus e raised to the power minus 1 into 5 by 2 that is further equal to 1 minus we are given the value of e raised to the power minus 1 in the question as 0.3679 so we'll use it here so we have 1 minus 0.3679 into 5 by 2 that is further equal to 1 minus 0 point we'll multiply these two terms to 0.91975 which is further equal to 0.8025 so this is the required answer to the session so hope you understood it well and enjoyed it too have a nice day