Question

q30.) sienna has a bag of 10 marbles. five marbles are blue, four marbles are red, and 1 marble is yellow. sienna draws two marbles from the bag without replacing the marble. what is the probability of drawing two of the same - colored marbles?

Explanation:

Step1: Calculate probability of two - yellow marbles

The probability of drawing a yellow marble on the first draw is $\frac{1}{10}$, and on the second draw (without replacement) is $\frac{0}{9}$. So the probability of two - yellow marbles is $\frac{1}{10}\times\frac{0}{9}=0$.

Step2: Calculate probability of two - red marbles

The probability of drawing a red marble on the first draw is $\frac{4}{10}$, and on the second draw (without replacement) is $\frac{3}{9}$. So the probability of two - red marbles is $\frac{4}{10}\times\frac{3}{9}=\frac{12}{90}$.

Step3: Calculate probability of two - blue marbles

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

Step4: Calculate total probability of same - color marbles

Add the probabilities of getting two - red and two - blue marbles. $P = 0+\frac{12}{90}+\frac{20}{90}=\frac{12 + 20}{90}=\frac{32}{90}=\frac{16}{45}$.

Answer:

$\frac{16}{45}$