Question 1084512: There are ten cards labelled 1 to 10. Jacky takes out two cards without replacing them. Find the probability that both show even numbers.
Thanks! Much appreciated.
Found 2 solutions by Theo, jim_thompson5910:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the cards are numbered 1 to 10.
there are 5 odd numbers and 5 even numbers.
the odd numbers are 1,3,5,7,9
the even numbers are 2,4,6,8,10
the probability of getting an even number on the first draw is 5/10.
assuming that an even number was drawn, then the probability of getting an even number on the second draw is 4/9.
this is because you drew one of the even numbers from the pot so there are 4 even numbers left and you drew one of ten numbers from the pot so there are 9 numbers left.
therefore, the probability of getting an even number on both draws is 5/10 * 4/9 = 20/90 = 2/9.
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! For problems like these, I find it helps to make a table like this one (shown below):
Table generated with Excel. Free alternative programs (such as OpenOffice) can do the same thing.
The top row represents the possible choices for the first draw.
The left border of values represent the choices for the second draw.
Any ordered pair of the form (x,y) represents a possible outcome for both cards.
For instance, in cell D9 we have the ordered pair (x,y) = (2,7) meaning that x = 2 is the first value drawn and y = 7 is the next value.
The other ordered pairs in the table are to be read in this similar way.
Note: Something like (x,y) = (2,2) is NOT possible because once we pick x = 2, we don't replace it.
It would be impossible to draw '2' again so the choices for y would go from {1,2,3,4,5,6,7,8,9,10} to {1,3,4,5,6,7,8,9,10}.
Whenever this sort of event happens, I will mark it as NA (as seen in the table above)
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Now go through the table and record all of the instances where BOTH x and y are even numbers
Here is that list of outcomes highlighted with double asterisks on each side
That highlighted list of ordered pairs is
(4,2)
(6,2)
(8,2)
(10,2)
(2,4)
(6,4)
(8,4)
(10,4)
(2,6)
(4,6)
(8,6)
(10,6)
(2,8)
(4,8)
(6,8)
(10,8)
(2,10)
(4,10)
(6,10)
(8,10)
There are 20 values in the list above.
There would be 10*10 = 100 outcomes if replacements were made, but no replacements are made meaning we have 10 copies of "NA" to subtract out. So we have 100-10 = 90 outcomes total.
Dividing the values (20 and 90) we get: 20/90 = 2/9 = 0.222222 = 22.2222%
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Final Answer as a fraction: 2/9 (this is exact)
Final Answer as a decimal value: 0.222222 (this is approximate)
Final Answer as a percentage: 22.2222% (this is approximate)
Notes:
* Use a calculator, or long division, to go from the fraction 2/9 to the decimal 0.222222
* To go from the decimal value to the percentage, move the decimal point 2 spots to the right.
* The three answer formats all represent the same idea just expressed different ways.
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