Download Lesson 6 - Hypergeometric Distribution TI-83

Statistics and the TI-83
Lesson 7
Hypergeometric Distribution
Hyper-geometric Distribution:
a
C x  N a Cn x
N Cn
 N: size of the population
 n: size of sample selected
 a: number in the population with a given characteristic
 N-a: number in the population without given characteristic
 x: number in the sample of size n with given characteristic
 n-x: number in the sample without the given characteristic
Exercise 1. A committee of 7 people is selected at random from a group of 8 men and 9
women. What is the probability that the committee will consists of 3 men and 4 women?.
8
answer:

8
C3 9 C 4
17 C 7
MATH
MATH

PRB
PRB
3
3
n
n
C r 3  9 MATH
Cr 7
ENTER
PRB
3
n
Cr 4 
ENT
17
answer .3628136569
MATH 1 ENTER
answer:
882
2431
Exercise 2. Find the probability of selecting at random (without replacement) 9 marbles (5 red
marbles and 4 blue) from a bag that contains 10 red marbles and 15 blue marbles.
 10 MATH
PRB 3 n C r 5  15 MATH
PRB 3 n C r 4 
25 MATH

PRB
3
MATH 1 ENTER
n
Cr 9
ENTER
ENTER
answer .1683721044
answer: .1683721044
Exercise 3. Find the probability of selecting at random (without replacement) 9 marbles (5 red
marbles and 4 blue) from a bag that contains 10 red marbles 15 blue marbles and 5 green
marbles.

10
MATH
5 MATH
PRB
PRB
3
3
n
n
C r 5  15 MATH
C r 0  30 MATH
PRB
PRB
.0240425242

MATH 1 ENTER
answer: . 0240425242
3
3
n
n
Cr 4 
C r 9 ENTER
answer
Exercise 4. A buyer must decide whether or not to accept a shipment of 40 parts. The decision
is based on inspecting a random sample of 5 parts. The shipment will be accepted If no
defective parts are found. Suppose that 4 of the parts are defective. What is the probability that
the shipment will be accepted?
4
answer:

4

MATH
C0 36 C5
40 C5
MATH
PRB
PRB
C r 0  36 MATH
3
n
n
Cr 5
3
ENTER
PRB
3
n
C r 5  40
answer: .5729292045
Exercise 5. A math team of three students to assess the school math standing is randomly formed from a
group of 2 sophomores, 12 juniors and 20 seniors.
a) Find the probability that the team is composed only of seniors.
20
C3 14 C0
34 C3

20
MATH


34 MATH
PRB
3
n
PRB
3
C r 3  14 MATH
n
PRB
3
n
Cr 0
C r 3 ENTER answer:.1905080214
b) Find the probability that both sophomores are on the team.
2
answer:
C 2 32 C1
34 C 3

2

 ENTER
MATH
PRB
3
n
34 MATH
C r 2  32 MATH
PRB
3
n
PRB
3
Cr 1
n
C r 3 ENTER
answer: 0.0053475936
c) Find the probability that all three classes are represented in the team.
answer:
2
C1 12 C1  20 C1
34 C 3

2

 20 MATH
MATH
0.080213937
PRB
3
PRB 3
n
C r 1  12 MATH
PRB
3
C r 1  34 MATH
PRB
3
n
n
n
Cr 1
C r 3 ENTER answer: