1. When solving similar problems, a tree diagram is a very useful method. Check the picture below for the solution of A:
the first pick can be either of the colors g, r, w or y, with a chance of 9/25, 7/25, 3/25 and 6/25 respectively.
After the first marble is yellow, now the second can be either of g, r, w, or y with chances 9/24, 7/24, 3/24, and 5/24 respectively.
Notice that the total number for the second choice is 25-1=24, since one is gone. In our case, one yellow, (this is why we now have 5/24)
So the P( that 1st is yellow, second is white) = (6/25)*(3/24)=3/100
B. P(both red)= (7/25)*(7/24)=49/600
C. P(1st red)=7/25
P(green, after replacement)=9/25
P(1.red,2.green)=(7/25)*(9/25)=63/625
the first pick can be either of the colors g, r, w or y, with a chance of 9/25, 7/25, 3/25 and 6/25 respectively.
After the first marble is yellow, now the second can be either of g, r, w, or y with chances 9/24, 7/24, 3/24, and 5/24 respectively.
Notice that the total number for the second choice is 25-1=24, since one is gone. In our case, one yellow, (this is why we now have 5/24)
So the P( that 1st is yellow, second is white) = (6/25)*(3/24)=3/100
B. P(both red)= (7/25)*(7/24)=49/600
C. P(1st red)=7/25
P(green, after replacement)=9/25
P(1.red,2.green)=(7/25)*(9/25)=63/625
