Question

A box contains 6 red and 8 green marbles. You reach in and remove 3 marbles all at once.

Answer 1

Answer:$\frac{5}{91},\frac{38}{182}$

Step-by-step explanation:

(a)Probability that these three marbles are all red

choosing 3 red out of 6 is given by $^6C_3$

and choosing 3 marble from 14 marbles=$^{14}C_3$

$Probability=\frac{^6C_3}{^{14}C_3}=\frac{5}{91}$

(b)All of same color

It is possible when they are of either red or green

For red it is $\frac{^6C_3}{^{14}C_3}$

For Green it is

$\frac{^8C_3}{^{14}C_3}$

total=$\frac{^6C_3}{^{14}C_3}+\frac{^6C_3}{^{14}C_3}$

=$\frac{38}{182}$