Question

In a box, there are 3 red marbles, 3 blue marbles and 7 green marbles. If 2 marbles are picked randomly, find the probability of picking two non-green marbles.

• A. $\dfrac{3}{26}$
• B. $\dfrac{5}{26}$
• C. $\dfrac{9}{26}$
• D. $\dfrac{7}{26}$

Hint:

When picking without replacement, use combinations: favourable $\binom{\text{wanted}}{2}$ over total $\binom{\text{all}}{2}$.

Answer 1

The Correct Option is B

Non-green marbles $=3+3=6$; Total marbles $=3+3+7=13$.
Required probability $=\dfrac{\binom{6}{2}}{\binom{13}{2}}=\dfrac{15}{78}=\dfrac{5}{26}$.
\(⇒\) Both chosen are from the 6 non-green marbles.