 Hi and welcome to the session. Let's work out the following question. The question says an insurance company has discovered that only 0.1% of the population is involved in a certain type of accident every year. If its 1000 policy holders are selected at random from the populations, what is the probability that not more than 5 of its clients are involved in such accidents next year? Use e raised to power minus 1 as 0.368. Let's start with the solution to this question. Here p is equal to 0.1 divided by 100 that is 0.1%. That is now n is 1000. So m will be equal to n into p that is 1 upon 1000 into 1000 that is equal to 1. Now we see that since p is very small and n is very large so we use the Poisson's distribution. So by Poisson's distribution probability at x equal to r will be equal to e raised to power minus m into m raised to power r divided by r factorial. Now we have to find the probability that not more than 5 of its clients are involved in such accidents. So we have to find probability x less than equal to 5 that is equal to probability at x equal to 0 plus probability at x equal to 1 plus probability at x equal to 2 plus probability at x equal to 3 plus probability at x equal to 4 plus probability at x equal to 5. This will be equal to e raised to the power –1 into 1 raised to the power 0, divide it by zero factorial. Plus e raised to the power minus 1 into 1 raised to the power 1 by 1 factorial. Plus e raised to the power minus 1 into 1 squared by 2 factorial. Plus, e raise to the power minus 1 into 1 cubed divided by our factorial. sorry 3 factorial plus e raised to power minus 1 into 1 raised to power 4 by 4 factorial plus e raised to power minus 1 into 1 raised to power 5 divided by 5 factorial. Now this is equal to e raised to power minus 1 into 1 plus 1 plus 1 by 2 plus 1 by 6 plus 1 by 24 plus 1 by 120 that is equal to e raised to power minus 1 into 240 plus 60 plus 20 plus 5 plus 1 divided by 120. We put the value of e raised to power minus 1 that is 0.368 into 326 divided by 120 and that is equal to 0.99973 which is approximately equal to 1. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.