1. ## Probability Problem

A bag contains 4 green balls, 7 red balls and 8 blue balls. Two balls are picked out at random. Find the probability that one green ball and one red ball are picked:

a) If the two balls were chosen simultaneously;

b) If the first ball was replaced before the second ball was picked.

2. Originally Posted by mr_motivator
A bag contains 4 green balls, 7 red balls and 8 blue balls. Two balls are picked out at random. Find the probability that one green ball and one red ball are picked:

a) If the two balls were chosen simultaneously;

b) If the first ball was replaced before the second ball was picked.

sorry , my mistake ..

(a) 4/19x7/18

(b) 4/19x7/19

I don't think this is the correct method.... any other suggestions?

4. Originally Posted by mr_motivator
I don't think this is the correct method.... any other suggestions?
Draw a tree diagram.

(a) $\left( \frac{4}{19}\right) \cdot \left( \frac{7}{18}\right) + \left( \frac{7}{19}\right) \cdot \left( \frac{4}{18}\right) = \, ....$

(b) $\left( \frac{4}{19}\right) \cdot \left( \frac{7}{19}\right) + \left( \frac{7}{19}\right) \cdot \left( \frac{4}{19}\right) = 2 \left( \frac{4}{19}\right) \cdot \left( \frac{7}{19}\right) = \, ....$

5. The first one is a hypergeometric...

${{4\choose 1}{7\choose 1}{8\choose 0}\over {19\choose 2}}$ $={(4)(7)(1)\over (19)(18)/2}\approx .16374269$.

The second is a trinomial...

${2\choose 1,1,0}\biggl({4\over 19}\biggr)^1\biggl({7\over 19}\biggr)^1\biggl({8\over 19}\biggr)^0$ $={2\over (1)(1)(1)}\biggl({4\over 19}\biggr)\biggl({7\over 19}\biggr)\approx .155124654$.