Question

A jar contains 6 blue, 4 red, and 2 green marbles. What is the probability that three blue marbles are drawn with out replacement?

Answer 1

Answer:  The required probability is 9.09%.

Step-by-step explanation:  Given that a jar contains 6 blue, 4 red, and 2 green marbles.

We are to find the probability that three blue marbles are drawn with out replacement.

Total number of marbles = 6 + 4 + 2 = 12.

After drawing one blue marble, we are left with total 11 marbles. And after drawing the second blue marble, we are left with total 10 marbles.

Therefore, the probability of drawing three blue marbles without replacement is given by

$p\\\\\\=\dfrac{^6C_1}{^{12}C_1}\times\dfrac{5C_1}{^{11}C_1}\times\dfrac{^4C_1}{^{10}C_1}\\\\\\=\dfrac{6}{12}\times\dfrac{5}{11}\times\dfrac{4}{10}\\\\\\=\dfrac{1}{11}\\\\\\=\dfrac{1}{11}\times100\%\\\\=9.09\%.$

Thus, the required probability is 9.09%.