Question

There are six chairs in a row. Person A picks one of the chairs at random. Then Person B picks a chair at random from the five chairs that remain. Find the chance that they pick chairs that are next to each other.

Answer 1

What have you tried? Is this a homework qn or online assessment?

Answer 2

I have tried 1/6*1/5 but turns out it is wrong.

Answer 3

Explain your reasoning please, I could offer a help from there.

Answer 4

My reasoning is since there are six chairs, the first pick at random could only be 1/6, and since five chairs will be left, the next pick at random should now be 1/5.

Answer 5

Have you learned conditional probability?

Answer 6

I have not; kindly explain please.

Answer 7

Okay, since you haven't learned it, I'll explain it another way. The first person have many choice of chairs?

Answer 8

Oh sorry if my poorly worded sentence annoys you. In how many ways can the first person pick a chair for himself?

Answer 9

six ways

Answer 10

Great. Then after that the second person comes in and choose a chair for himself, in how many ways can this be done?

Answer 11

five ways.

Answer 12

Multiply them out, you'll have the total number of ways 2 chairs can be chosen, right? That number must be saved for later use.

Answer 13

Now given 6 chairs IN A ROW (this is important), how many ways can you pick 2 that is next to each other?

Answer 14

I am confused here, but I think it will be one out of six twice, that is, one in six ways twice.

Answer 15

No. Imagine you have six chairs. Draw a circle containing any of two consecutive chairs, how many circles are there?

Answer 16

three.

Answer 17

You undercounted them.