Question

Please help I only have a few mins to answer

A bag contains 9 red marbles, 8 white marbles, and 10 green marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a redred marble and then a greengreen marble?
  

b. A bag contains 8 yellow marbles, 10 green marbles, and 9 white marbles. If two different marbles are drawn from the bag , what is the probability of drawing first a yellowyellow marble and then a whitewhite marble?
  

  

Answer 1

a)

We have 9 Red marbles, 8 White Marbles and 10 green Marbles, Total =27

If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a red marble and then a green marble?

$\frac{9}{27}*\frac{10}{27}=0.12345$

b)

We have 8 Yellow marbles, 10 Green Marbles and 9 White Marbles, Total =27

If two different marbles are drawn from the bag, what is the probability of drawing first a yellow marble and then a white marble?

$\frac{8}{27}*\frac{9}{27}=0.09876$

This can also be understood using combinatorics :

$\frac{\operatorname{nCr}\left(8,1\right)}{\operatorname{nCr}\left(27,1\right)}\cdot\frac{\operatorname{nCr}\left(9,1\right)}{\operatorname{nCr}\left(27,1\right)}=0.09876$