a bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. five marbles are…

Explanation:

Step1: Calculate total number of marbles

$10 + 15+5 + 20=50$ marbles.

Step2: Use combination formula for probability

The number of ways to choose 5 marbles out of 50 is $C(50,5)=\frac{50!}{5!(50 - 5)!}=\frac{50!}{5!45!}=\frac{50\times49\times48\times47\times46}{5\times4\times3\times2\times1}=2118760$. The number of ways to choose 2 blue marbles out of 20 is $C(20,2)=\frac{20!}{2!(20 - 2)!}=\frac{20\times19}{2\times1}=190$. The number of ways to choose the remaining $5 - 2 = 3$ non - blue marbles out of $50-20 = 30$ non - blue marbles is $C(30,3)=\frac{30!}{3!(30 - 3)!}=\frac{30\times29\times28}{3\times2\times1}=4060$. The number of ways to choose exactly 2 blue marbles out of 5 is $C(20,2)\times C(30,3)=190\times4060 = 771400$.

Step3: Calculate probability

The probability $P=\frac{C(20,2)\times C(30,3)}{C(50,5)}=\frac{771400}{2118760}\approx0.364$. Converting to percentage, $0.364\times100 = 36.4%\approx36%$.

Answer:

36%