Question

a bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. two marbles are drawn from the bag.
what is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?
0.02222
0.04444
0.08889
0.13333

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(5 + 2+1 + 2=10\)

Step2: Calculate number of ways to choose 2 marbles

Using combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), here \(n = 10\), \(r=2\). 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 orange marbles \(=2\), number of green marbles \(=2\). Using multiplication principle: \(C(2,1)\times C(2,1)=\frac{2!}{1!(2 - 1)!}\times\frac{2!}{1!(2 - 1)!}=2\times2 = 4\)

Step4: Calculate probability

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

Answer:

0.08889