Half-life and muon decay Imagine that we have a single muon. It has a life span of 2.2 microseconds on average. So normally, after that amount of time, the muon will decay.
Now imagine we have two groups of muons. Group A has 20 muons and the other group, B , 10 muons. Since muons have a half life of 2.2 microseconds, group A will lose 10 muons in that time but group B will lose 5 muons. Why is this so? If the a sinle muons decays in 2.2 microseconds, normally, all the muons should decay in that time as they are all muons and so decay in 2.2 microseconds. Group A lost more muons in the same time than group B. This can only be if the muons in group a decayed faster than the muons in group B. how can this be? Is the life of muons inversely proportional to the amount of muons present?  
 A: Imagine two groups of students, where group A has 20 members and group B has 10.  Each student flips a coin, and we find that 10 coins from group A and 5 coins from group B land face-up.
Does the probability of the coin landing face-up depend on the size of the group?  No, of course not.  The probability of a coin landing face-up is simply 1/2, which means that we'd expect to see it in about half of the coins in a group of any size.  Larger groups flip more heads because more coins are being tossed, that's all - and precisely the same is true for radioactive decay.
A: No, muon decay is a statistical process with a constant half life. After  2.2 microseconds there is a 50% chance that the muon has decayed. This means that on average half of the muons have decayed. For group A half is 10 and for B it is 5. Note that muons that are generated in the atmosphere by cosmic rays live much longer as they travel at near light speed. 
A: Imagine you had two group Bs each with 10 muons at the start.
According to your arithmetic both group Bs will have have lost 5 muons after 2.2 microseconds ie two groups of type B have lost 10 muons in total.
So two group Bs do exactly the same as one group A.
