Thread: Discrete Probability Distribution

from walpole 5.32

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that
a) all 4 will fire
b) at most 2 will not fire ?

I believe this is a hypergeometric distribution.
pls correct me if i am wrong.

a) since all 4 , i took P(x= 0) + .....P(x=4)
4C0 x 6C4 / 10C4 + 4C1 x 6C3 / 10C4 + .....
and i got 13/14. but this does not tally with the answer stated on my worksheet. where did i go wrong ?

b) at most 2 will not fire means P (X<=2) ?

Originally Posted by hazel

from walpole 5.32

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that
a) all 4 will fire
b) at most 2 will not fire ?

I believe this is a hypergeometric distribution. Mr F says: Correct.
pls correct me if i am wrong.

a) since all 4 , i took P(x= 0) + .....P(x=4)
4C0 x 6C4 / 10C4 + 4C1 x 6C3 / 10C4 + .....
and i got 13/14. but this does not tally with the answer stated on my worksheet. where did i go wrong ?

b) at most 2 will not fire means P (X<=2) ?

You must define the random variable before doing anything else.

Let X be the random variable 'number of defective missiles in sample'.
X ~ Hypergeometric(N = 10, n = 4, D = 3).

a) Calculate Pr(X = 0).

b) Calculate Pr(X = 0) + Pr(X = 1) + Pr(X = 2) = 1 - Pr(X = 3) - Pr(X = 4).

Hello, Hazel!

From a lot of 10 missiles, 4 are selected at random and fired.
If the lot contains 3 defective missiles that will not fire,
what is the probability that:

a) all 4 will fire?

Let: .

There are: . possible samples.

There are: . samples with 4 G's.

Therefore: .

b) at most 2 will not fire ?

The opposite of "at most 2 D's" is "3 D's (and 1 G)".

The number of samples with 3 D's and 1 G is: .

Hence: .

Therefore: .

Originally Posted by Soroban

Hello, Hazel!


The opposite of "at most 2 D's" is "3 D's (and 1 G)".

The number of samples with 3 D's and 1 G is: .

Hence: .

Therefore: .

But for at most 2 will fire :
means 1G, 3D and also 2G 2D right ?