a.
[tex] \frac{7purple}{9total} * \frac{2white}{8total} \\ \frac{14}{72} \\ =0.194[/tex]
The denominator of the second number goes down one because you aren't replacing the initial marble pulled, making the amount of marbles in the bag go down, but not affecting the white count because you pulled a purple marble.
b.
[tex] \frac{2white}{9total} * \frac{1white}{8total} \\ \frac{2}{72} \\ =0.278[/tex]
The same can be said about the denominator for this problem, but not the numerator. The numerator must go down one number as well, because you already chose one white marble, taking one of the white marbles out of the bag, leaving you with one solitary, white marble.
c.
Chance of selecting two purple marbles:
[tex] \frac{7purple}{9total} * \frac{6purple}{8total} \\ \frac{42}{72} \\ =0.583[/tex]
Chance of selecting two white marbles:
[tex]\frac{2white}{9total} * \frac{1white}{8total} \\ \frac{2}{72} \\ =0.278[/tex]
Chance of selecting two purple vs. Chance of Selecting 2 white:
0.583>0.278.
It is more likely to select 2 purple marbles.
Hope this helps!
