a bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. two marbles…

Answer:

C. 0.08889

Explanation:

Step1: Calculate total number of marbles

$5 + 2+1 + 2=10$

Step2: Calculate number of ways to choose 2 marbles

Using combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 10$ and $r = 2$. So $C(10,2)=\frac{10!}{2!(10 - 2)!}=\frac{10\times9}{2\times1}=45$

Step3: Calculate number of ways to choose 1 orange and 1 green marble

Number of ways to choose 1 orange out of 2 is $C(2,1)=\frac{2!}{1!(2 - 1)!}=2$. Number of ways to choose 1 green out of 2 is $C(2,1)=\frac{2!}{1!(2 - 1)!}=2$. By multiplication - principle, number of ways to choose 1 orange and 1 green is $C(2,1)\times C(2,1)=2\times2 = 4$

Step4: Calculate probability

Probability $P=\frac{4}{45}\approx0.08889$