Answer :
Answer: [tex]B.\ \dfrac{12}{35}[/tex]
Step-by-step explanation:
Given : The bag that contains six blue marbles and nine red marbles.
Number of red marbles = 9
Total marbles = 6+9=15
Total outcomes : The number of combinations of drawing 2 balls from 15 :-
[tex]^{15}C_2=\dfrac{15!}{2!(15-2)!}=105[/tex]
Favorable outcomes : The number of combinations of drawing 2 red balls from 9 :-
[tex]^{9}C_2=\dfrac{9!}{2!(9-2)!}=36[/tex]
Now, the probability that both marbles drawn are red :
[tex]\dfrac{\text{favorable outcomes}}{\text{Total outcomes }}=\dfrac{36}{105}\\\\ =\dfrac{12}{35}[/tex] [divided numerator and denominator by 3]
hence, the required probability = [tex]\ \dfrac{12}{35}[/tex]