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 = \(\dfrac{\binom{6}{2}}{\binom{13}{2}}=\dfrac{15}{78}=\dfrac{5}{26}\).
\(\Rightarrow\) Both marbles selected are from the 6 non-green marbles.
\boxed{\text{Probability}=\dfrac{5}{26}}