Answer:
a)
Red = 4 marbles
Green = 6 marbles
Blue = 8 marbles
b) i)
P(BB) = 16/81
b) ii)
P(they are of the same color) = 116/324
Step-by-step explanation:
Given:
Red : Green: Blue = 2:3:4
First marble is blue: 8/18 (since there are 8 blue marbles out of 18)
The second marble is blue (replaced): 8/18
The probability of both being blue: The first
P(BB) = 8/18 * 8/18
= 64/324 = 16/81
Note: P(BB) Means the probability of two blue marbles being selected
b ii)
The probability that they are of the same color, which means they may be both red, both green, or both blue
We need to find the probability of each marble color and then add it together
P(RR) = 4/18 * 4/18 = 16/324 = 4/81
P(GG) = 6/18 * 6/18 = 36/324 = 1/9
P(BB) = 8/18 * 8/18 = 64/324 = 16/81 (From b i)
Therefore, P(they are of the same color)
= 16/324 + 36/324 + 64/324
= 116/324