# probability - Does it matter who goes ﬁrst?

Three students have only one ticket to the superbowl. They will decide who is going in the following way. They will ask someone else to put the ticket in one of three boxes. One of them will pick a box and open it. If the ticket is in the box, he gets it, otherwise he is out and the box removed. The second person picks a box from the two that are left and opens it. If the ticket is in the box, he gets it, otherwise he is out and the box removed, leaving the last person to pick be the one who gets the ticket. Does it matter who goes ﬁrst?

My thoughts:

I think it matters.

If A goes first, his chance of getting the ticket is $1/3$. While the chance of b or c to get the ticket is $1/6$

So it matters.

Is it right? Does this question relates to Conditional or Marginal probabilities?

• Note $1/3 + 1/6 + 1/6 \neq 1$, which should tell you that the probabilities can't be $1/3$, $1/6$, and $1/3$. See? – Quinn Culver Sep 8 '16 at 11:39

$$\text{Probability that the first person gets it}=\frac{1}{3}$$ $$\text{Probability that the second person gets it}=\text{Probability that the first person does not get it}\times\text{Probability that the second person gets it in his turn}=\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}$$
Similarly, $$\text{Probability that the third person gets it}=1-\frac{2}{3}=\frac{1}{3}$$