Question

A girl scout and her mom are setting up a table to sell cookies in front of a
grocery store. They have available 6 boxes of Samoas, 6 boxes of Tagalons, 2 boxes of
Do-si-dos, and 6 boxes of Trefoils. Each box sells for $5.

Suppose that, immediately after they finish setting up, the first customer shows up, and he
purchases 4 boxes of cookies. Determine the probability distribution function for the number of
Tagalons purchased.

Draw the cumulative distribution function for the number of Tagalons purchased.

Answer 1

total boxes = 6+6+2+6=20

boxes of tagalons = 6

boxes that are not tagalons = 20-6 = 14

x : no. of tagalons boxes out of 4

P(x) = (select x tagalon boxes from 6)*(select (4-x) boxes that are not tagalons) / (select 4 boxes from 20)

= 6Cx * 14C(4-x) / 20C4

= 6Cx * 14C(4-x) / 4845

x	P(x)
0	6C0 * 14C(4) / 4845 = 0.2066
1	6C1 * 14C(3) / 4845 = 0.4508
2	6C2 * 14C(2) / 4845 = 0.2817
3	6C3 * 14C(1) / 4845 = 0.0578
4	6C4 * 14C(0) / 4845 = 0.0031

cummulative distribution :

X	P(x<=X)
0	0.2066
1	0.4508+0.2066 = 0.6574
2	0.2817+0.4508+0.2066 = 0.9391
3	0.0578+0.2817+0.4508+0.2066 = 0.9969
4	0.0031+0.0578+0.2817+0.4508+0.2066 = 1

cummulative distribution graph :