Answer: The required probability of getting two green marbles is 49.45%.
Step-by-step explanation: Given that a bag contains 10 green marbles and 4 yellow marbles. Two marbles are chosen at random, one at a time and without replacement.
We are to find the probability of getting two green marbles.
Let S denote the sample space for the experiment of choosing a marble from the bag and A denote the event of getting a green marble.
The, n(S) = 10 + 4 = 14 and n(A) = 10.
So, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{10}{14}=\dfrac{5}{7}.[/tex]
After getting one green marble and not replacing, let S' denote the sample space for the experiment of choosing a marble from the bag
and
let B denote the event of getting another green marble.
Then, n(S') = 14 - 1 = 13 and n(B) = 10 - 1 = 9.
Then, the probability of getting two green marbles is given by
[tex]P\\\\=P(A)\times P(B)\\\\=\dfrac{5}{7}\times\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{5}{7}\times\dfrac{9}{13}\\\\\\=\dfrac{45}{91}\times100\%\\\\=49.45\%.[/tex]
Thus, the required probability of getting two marbles is 49.45%.
