A bag contains 5 red, 7 yellow, 8 green markers. What is the p(two green markers) will be chosen if the markers are not replaced as they are chosen?
probability of first green
= 8/20
probability of second green = 7/19
so
(8/20)(7/19)
To find the probability of choosing two green markers without replacement, you need to first calculate the total number of ways you can choose two markers from the total set of markers.
To solve this problem, we can use combinations. The formula for calculating combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items to choose from
- r is the number of items you want to choose
- ! denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1)
Now, let's apply this formula to solve the problem.
The bag contains a total of 5 red, 7 yellow, and 8 green markers. In this case, we want to choose 2 green markers out of the total 20 markers in the bag.
The formula for the number of ways to choose 2 green markers can be written as:
C(8, 2) = 8! / (2!(8-2)!)
Simplifying this expression:
C(8, 2) = 8! / (2! × 6!)
= (8 × 7 × 6!)/(2! × 6!)
= (8 × 7) / (2 × 1)
= 56 / 2
= 28
So, there are 28 total ways to choose 2 green markers from the given bag.
To calculate the probability, we need to divide the number of favorable outcomes (two green markers) by the total number of possible outcomes (choosing any two markers).
Therefore, the probability of choosing two green markers is:
P(two green markers) = Number of ways to choose 2 green markers / Total number of ways to choose 2 markers
P(two green markers) = 28 / Total number of ways to choose 2 markers
Since we have already calculated the total number of ways to choose 2 markers (28), we can substitute it into the formula:
P(two green markers) = 28 / 28
= 1
Therefore, the probability of choosing two green markers from the bag without replacement is 1.