Question

A box contains 8 red balls, 4 green balls, and 3 blue balls. You pull 2 balls from the box (one at a time) WITHOUT replacement.

**LEAVE ALL ANSWERS AS FRACTIONS**

Find the probability of the following:

a.) P(Red on 1st ball AND Red on 2nd ball) =

b.) P(Green on 1st ball AND Red on 2nd ball) =

c.) P(Blue on 1st ball AND Green on 2nd ball) =

d.) What is the probability of drawing 2 green balls in your 2 pulls?

e.) What is the probability of selecting a red ball on your second pull, given a red ball was already selected on the first pull?

f.) What is the probability of drawing one red ball and one green ball (in either order)?

g.) What is the probability or selecting two balls of the same color?

h.) What is the probability or selecting two balls of different colors?

Answer 1

Solution:

Given:A box contains 8 red balls, 4 green balls, and 3 blue balls.

Thus total balls = 8 + 4 + 3 =15

2 balls are pulled from the box (one at a time) without replacement.

Part a) P(Red on 1st ball AND Red on 2nd ball) =.......?

P(Red on 1st ball AND Red on 2nd ball) =P(Red) x P( Red)

P(Red on 1st ball AND Red on 2nd ball) = (8/15) x ( 7 /14)

P(Red on 1st ball AND Red on 2nd ball) = (8/15) x ( 1/2)

P(Red on 1st ball AND Red on 2nd ball) = 8 /30

P(Red on 1st ball AND Red on 2nd ball) = 4/15

Part b) P(Green on 1st ball AND Red on 2nd ball) =.......?

P(Green on 1st ball AND Red on 2nd ball) =P( Green ) x P( Red)

P(Green on 1st ball AND Red on 2nd ball) = (4/15 ) x ( 8/14)

P(Green on 1st ball AND Red on 2nd ball) = (4x8) /(15x14)

P(Green on 1st ball AND Red on 2nd ball) =32 / 210

P(Green on 1st ball AND Red on 2nd ball) = 16/105

Part c)P(Blue on 1st ball AND Green on 2nd ball) =.......?

P(Blue on 1st ball AND Green on 2nd ball) = P( Blue ) x P( Green )

P(Blue on 1st ball AND Green on 2nd ball) = ( 3 /15 ) x ( 4/14)

P(Blue on 1st ball AND Green on 2nd ball) = ( 1 /5 ) x ( 2/7)

P(Blue on 1st ball AND Green on 2nd ball) = 2/35

Part d) What is the probability of drawing 2 green balls in your 2 pulls?
P( Green on 1st ball AND Green on 2nd ball) =...........?

P( Green on 1st ball AND Green on 2nd ball) =(4/15) x ( 3/14)

P( Green on 1st ball AND Green on 2nd ball) = (4x3) / ( 15x14)

P( Green on 1st ball AND Green on 2nd ball) = 12 / 210

P( Green on 1st ball AND Green on 2nd ball) = 2 / 35