Let’s say the person chooses those numbers randomly and in the same way they are drawn (e.g. no replacement so number 1 can only be chosen once for the white balls).
The black ball is there just to get the exact probability estimate for the Mega Millions lottery.
To answer your question it comes from the Mega Millions lottery which draws 5 white balls and 1 black ball. And I’m curious to know what is probability I get first two numbers right.
Suppose I draw 5 numbers uniformly at random from 1 to 70, and suppose I do so twice. What is the probability that the smallest two numbers match, and no others?
So let a1<a2<a3<a4<a5 be the number from one draw, and let b1<b2<b3<b4<b5 be the number from the other draw. What is the probability that a1=b1, a2=b2, and a3, a4, a5, b3, b4, b5 are all different.
Is that your question?
How accurately do you need to know the answer? You can get an approximation quite quickly by simulation ... an exact answer will be horrible.
Edit: OK, I have answers, but it would be useful to know how accurately you need your answer.
The black ball is there just to get the exact probability estimate for the Mega Millions lottery.
To answer your question it comes from the Mega Millions lottery which draws 5 white balls and 1 black ball. And I’m curious to know what is probability I get first two numbers right.