There are 25.7 million people wanting to get the rare toy but there only 100 whats the chance of you getting one?

Question

.whats the chance of me getting it

Answer 1

Let's suppose that each of the 27.5M people has only 1 ticket to win a toy. If you are one of these people then the probability of not having a winning ticket is (27,500,000-1)/27,500,000 (almost 1). For this failure to occur 100 times (because there are 100 toys) is ((27,500,000-1)/27,500,000)¹⁰⁰. So the probability of winning a toy is 1 less than this.

Probability of failure=(27499999/27500000)¹⁰⁰.

We can use logarithms to compute this:

100log₁₀(27499999/27500000)=-1.5793×10^-6.

10^{-1.5793×10⁻⁶}=0.9999963636 approx. (probability of failure)

Chances of winning 1-0.9999963636=0.0000036364 or about 1 in 275,000.5.

Note that this is almost the same as 100/27,500,000.

Another way of calculating this is to use the binomial expansion:

[(27500000-1)/27500000]¹⁰⁰=(1-1/27500000)¹⁰⁰=1-100/27500000 approx.

So 1-(1-100/27500000)=100/27500000=1/275000.