00:01
In this question we have been given about the counting rate of a radioactive sample and here we can say that this is a question of homogeneous, let us here write it will be ous and then here we can say poison distribution.
00:18
So it can be here written as poison and then here it will be dis tri and then it is here bu tion.
00:30
So now we can say that homogeneous mean that the average counting rate is constant throughout the experiment.
00:38
So the basic we can say poison probability is for a single value and that is here going to be equals to lambda raised to the power n and then here it is e raised to the power negative lambda divided with n factorial.
00:55
So here we can say that in order to find out the value of probability such that x is less than n, it will be here equals to summation from i is equals to 0 to it will be here n minus 1, we can write here that it will be probability of x is equals to i.
01:15
So here we can say that lambda raised to the power is 0 and 0 factorial is 1.
01:22
So remember that and hence we can say that it will be here such that lambda value that is expected number of events in any given time interval for 10 seconds will be here equals to we can write it as 81 counts and remember that in this very case the value of n will be equals to 72 counts.
01:46
So based on this very information we can say that the value of probability such that x is here less than 72 it will be here equals to 0 .14495 and then here it is 1185 and then it will be here 332563.
02:08
So we can put this very value inside a box in order to highlight it because we will be using this very value to compare at last and it is also the answer...