Question

q 29.) a box contains 5 black markers, 3 red markers, and 2 green markers. jill randomly chooses two markers from the box. what is the probability that jill chose 2 markers of the same color? 1st choice 2nd choice

Explanation:

Step1: Calculate probability of two - green

The probability of choosing a green marker on the first draw is $\frac{2}{10}$, and on the second draw (without replacement) is $\frac{1}{9}$. So the probability of two - green is $\frac{2}{10}\times\frac{1}{9}=\frac{2}{90}$.

Step2: Calculate probability of two - red

The probability of choosing a red marker on the first draw is $\frac{3}{10}$, and on the second draw (without replacement) is $\frac{2}{9}$. So the probability of two - red is $\frac{3}{10}\times\frac{2}{9}=\frac{6}{90}$.

Step3: Calculate probability of two - black

The probability of choosing a black marker on the first draw is $\frac{5}{10}$, and on the second draw (without replacement) is $\frac{4}{9}$. So the probability of two - black is $\frac{5}{10}\times\frac{4}{9}=\frac{20}{90}$.

Step4: Calculate total probability

The probability that the two markers are of the same color is the sum of the probabilities of two - green, two - red, and two - black. So $P=\frac{2 + 6+20}{90}=\frac{28}{90}=\frac{14}{45}$.

Answer:

$\frac{14}{45}$