A bag contains 5 red, 7 yellow, 8 green, and 3 blue markers. What is the p(two green markers) will be chosen if the markers are not replaced as they are chosen?
I just did this :(
slightly different numbers, same problem
http://www.jiskha.com/display.cgi?id=1441141046
To find the probability of choosing two green markers without replacement, we need to calculate the ratio of the favorable outcomes (two green markers) to the total number of possible outcomes.
First, let's determine the total number of markers in the bag:
Total markers = number of red markers + number of yellow markers + number of green markers + number of blue markers
Total markers = 5 + 7 + 8 + 3 = 23 markers
Next, we calculate the number of ways to choose two green markers out of the eight green markers in the bag:
Number of ways to choose two green markers = (number of green markers) choose (number of green markers to be selected)
Number of ways to choose two green markers = 8 choose 2
We can use the formula for combinations to calculate this:
n choose r = n! / (r! * (n-r)!)
Applying this formula:
8 choose 2 = 8! / (2! * (8-2)!)
Simplifying:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320
2! = 2 * 1 = 2
(8-2)! = 6!
8 choose 2 = 40320 / (2 * 720) = 40320 / 1440 = 28
Therefore, there are 28 different ways to choose two green markers out of the bag.
Now, we need to calculate the total number of ways to choose any two markers from the bag, without replacement:
Total number of ways to choose any two markers = (total number of markers) choose (number of markers to be selected)
Total number of ways to choose any two markers = 23 choose 2
Using the combination formula:
23 choose 2 = 23! / (2! * (23-2)!)
23! = 23 * 22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
2! = 2 * 1
(23-2)! = 21!
23 choose 2 = (23 * 22 * 21!) / (2! * 21!)
= (23 * 22) / (2 * 1)
= 23 * 11
= 253
Therefore, there are 253 different ways to choose any two markers from the bag.
Finally, we can calculate the probability of choosing two green markers:
Probability = (Number of ways to choose two green markers) / (Total number of ways to choose any two markers)
Probability = 28 / 253
Thus, the probability of choosing two green markers without replacement from the bag is 28/253, or approximately 0.1106, or approximately 11.06%.