A box contains 6 red and 8 green marbles. You reach in and remove 3 marbles all at once.(a) Find the probability that these 3 marbles are all red. (Enter your answer as a fraction.)(b) Find the probability that these 3 marbles are all of the same color. (Enter your answer as a fraction.)
Accepted Solution
A:
Answer:[tex] \frac{5}{91},\frac{38}{182} [/tex]Step-by-step explanation:(a)Probability that these three marbles are all redchoosing 3 red out of 6 is given by [tex]^6C_3[/tex]and choosing 3 marble from 14 marbles=[tex]^{14}C_3[/tex][tex]Probability=\frac{^6C_3}{^{14}C_3}=\frac{5}{91}[/tex](b)All of same colorIt is possible when they are of either red or greenFor red it is [tex]\frac{^6C_3}{^{14}C_3}[/tex]For Green it is[tex]\frac{^8C_3}{^{14}C_3}[/tex]total=[tex]\frac{^6C_3}{^{14}C_3}+\frac{^6C_3}{^{14}C_3}[/tex]=[tex] \frac{38}{182} [/tex]