Need help with my stats homework!

Question

Nine agricultural plots for an experiment are laid out in a square grid (so the picture shown is a 3 by 3 square grid).  Three plots are selected at random.

 

A)  find the probability that all 3 are in the same row.

 

B)  find the probability that all 3 are in different rows.

 

Thanks!

Answer 1

A. During the selection process, the first plot can be in any row.  But the second plot has to be the same row.  At that point there are only 2 plots left in the same row, out of 8 left in the entire grid.  So the probability that the second one will be in the same row as the first is 2/8 = 1/4.

 

The third selection then has to be the one remaining plot in the same row.  At that point, there are 7 left, so the probability that the last one will be in the same row is 1/7.

 

So the probability that all three will be in the same row is (1/4) * (1/7) = 1/28.

 

B.  Again the first plot can be in any row.  The second plot has to be in a DIFFERENT row.  There are 6 plots available in the other two rows, out of a total of 8.  So the probability that the second plot is in a different row from the first is 6/8 = 3/4.

 

And then the third plot would have to be in a different row from the first AND a different row from the second.  That is, it would have to be in the other row.  There are 3 plots available in that row, and 7 all together.  So the probability that the third plot would be in a different row from both of the first two is 3/7.

 

So the probability that all three are in different rows is (3/4) * (3/7) = 9/28.