Answer:
5.1%
Step-by-step explanation:
A bag contains 7 red marbles, 6 blue marbles and 4 green marbles, 17 marbles in total.
Number of red marbles = 7
Number of all marbles = 17
Number of choices 3 red marbles out of 7 red marbles [tex]=C^7_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7!}{3!\cdot 4!}=35[/tex]
Number of choices 3 marbles out of 17 marbles [tex]=C^{17}_3=\dfrac{17!}{3!(17-3)!}=\dfrac{17!}{3!\cdot 14!}=17\cdot 8\cdot 5=680[/tex]
The probability that all three marbles drawn will be red is
[tex]\dfrac{35}{680}=\dfrac{7}{136}\approx 0.0514705\approx 5.1\%[/tex]
