1)
white (w) marble
yellow (y) marble
green (g) marble
red (r) marble
Pw+Pw+Pg+Pr=1 (Eq. 1 )
w+y+g+r=12 (Eq. 2)
Answer: There are 12 marbles in the bag. SInce the question says the bag contains 12 marbles.
2)
a) Pw+Py = Pg
w + y = g (Eq. 3)
b) Pw = 10/40 = 1/4
If P = 1/4, if we have 12 marbles, P=3/12
Then, we know that we have 3 white marbles
Answer: There are 3 white marbles in the bag.
3) Pr = 1/5. Considering that 2 marbles were removed, we have 10 markles. The Pr=2/10.
Answer: Thus, we have 2 balls red.
4) From 12 marbles, we already know that 3 are white and 2 are red.
Then: 12-3-2= 7
Answer: 7 marbles are green or yellow.
5)
From question 4 , we know that;
y + g = 7
y = 7 - g (Eq. 4)
And from Eq. 3
w + y = g
3 + y = g
Substituing Eq. 4 in Eq. 3:
3 + 7 - g = g
10 = 2g
10/2 = g
g = 5
And:
y = 7 - g
y = 7-5
y = 2
The numeratiors are:
3 (Pw), 2 (Py), 5 (Pg)
5) 2 = yellow marbles
5 = green marbles