Probability

1. A big contains 5 red balls, some green balls and blue balls. The number of green balls and blue balls are in a ratio of 2:3. A ball is drawn at random from the bag. Given that the probability of drawing a green ball is 3/10, find the number of green balls in the bag.

Asssume
the number of green balls ini the bag is 2n
the numberof blue balls is 3n
then
2n / (5 + 2n + 3n) = 3/10
15 + 15n = 20n
n = 3
Hence,
the number of green balls in the bag is 6


2. Eric is playing a throwing game. In the game, a token of radius 2cm has to be thwoen onto square grids of sides 8cm. If the token lands completely inside the square, the player wins. Find the probaility that eric wins in one round.
As follow,
the probaility is
P = (8- 2 x 2)2 / 82
= 1 / 4

1. T = total no of ball
G = no of green ball
B = no of blue ball

G + B + 5 = T

G/T = 3/10 --> T = 10G/3
G/B = 2/3 --> B = 3G/2

substitute into 1st equation
--> G + 3G/2 + 5 = 10G/3

--> 10G/3 - 3G/2 - G = 5 (whole equation x 6)
--> 20G - 9G - 6G = 30
--> G = 6