In: Statistics and Probability
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.
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 :