Question 1083673: Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.
What is the probability of selecting an even number then a number greater than 7?
3/25
2/15
1/6
8/45
Found 3 solutions by josmiceli, MathTherapy, jim_thompson5910:
Answer by josmiceli(19441)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! Create a table such as this one
to list out the entire sample space
The entries NA mean "not applicable". They represent the cases of picking the same number twice. This isn't possible because the slips of paper aren't replaced.
Each ordered pair represents a combination of selections. For example, (7,10) means that you picked the slip "7" first and the slip "10" next.
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Go through this table and highlight all of the cells that meet the following conditions:
(1) The first selection is even. In other words, the x coordinate of the ordered pair is even
(2) The second selection is greater than 7. Look for y values of the ordered pair that are larger than 7
Both conditions (1) AND (2) must be true at the same time.
Here's what the highlighting would look like
There are 13 highlighted cells out of 90 different ways to pick 2 slips of paper (from a pool of 10 without replacement)
So the answer should be 13/90. Unfortunately this answer isn't listed so I'm not sure what went wrong. I might have made an error somewhere, so I'd get a second opinion. It's also possible that the teacher made a typo somewhere.
Note: your teacher may be thinking 15/90 = 1/6 but that's not possible since we have 13 highlighted cells, not 15. The two cells (8,8) and (10,10) would be highlighted if we could replace the slips, but we can't.
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