Maria has cloth in four colors (red, blue, green, yellow) and two styles (large, small)
for the school logo. The flag she is making will have two different stripes with white
in the middle and the logo. What is the probability that her design will have red and
blue stripes and the large logo?
The number of different flags she can make is
4x3x2 which is 24
The one you describe is one of those, so that prob is 1/24
To calculate the probability of Maria's design having red and blue stripes with the large logo, we need to find the ratio of the number of favorable outcomes (red and blue stripes with the large logo) to the number of possible outcomes.
First, let's determine the number of possible outcomes for the stripes. Since Maria has four colors to choose from (red, blue, green, and yellow), and she needs two different stripes (red and blue), we can use the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of colors available, and r is the number of stripes needed.
In this case, n = 4 and r = 2. Plugging in these values:
C(4, 2) = 4! / (2!(4-2)!)
C(4, 2) = 4! / (2!2!)
C(4, 2) = (4 * 3 * 2!) / (2! * 2!)
C(4, 2) = (4 * 3) / (2)
C(4, 2) = 6
So, there are six possible combinations of two different colored stripes.
Now, let's determine the number of possible outcomes for the logo style. Since Maria has two styles to choose from (large and small), there are two possible outcomes.
Multiplying the number of stripe outcomes (6) by the number of logo style outcomes (2), we get the total number of possible outcomes:
Total possible outcomes = 6 * 2 = 12
To calculate the probability, we need to divide the number of favorable outcomes by the total possible outcomes. In this case, we want red and blue stripes with the large logo, so there is only one favorable outcome.
Probability = Favorable outcomes / Total possible outcomes
Probability = 1 / 12
Therefore, the probability that Maria's design will have red and blue stripes with the large logo is 1/12 or approximately 0.0833, which is about 8.33%.