Binomial distribution: subscriptions to cable TV

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peggyskold

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Can anyone help me with this. In this example:

Fifty-nine percent of households in the US subscribe to cable TV. You randomly select six households and ask each if they subscribe to cable TV. Construct a probability distirbution for the random variable x.

I understand how to get n=6, p=0.59 and q=0.41 and the x=0, 1,2,3,4,5,6 but I am confused on how to get P(0)=0.005, P(1)=0.041, etc, etc. what is the most straightforward way to compute this.

I am having trouble with the Binomial Probability Formula:

in this example where p=0.25, q=0.75 and n=7 x=0,1,2,3,4,5,6,7
P(2)=21(0.25)^2 (0.75)^5=0.3115 (the ^ sybolizes the exponent here)

Where do they get the (21) that they multiply here?
Thanks
Peggy
 
peggyskold said:
Can anyone help me with this. In this example:

Fifty-nine percent of households in the US subscribe to cable TV. You randomly select six households and ask each if they subscribe to cable TV. Construct a probability distirbution for the random variable x.

I understand how to get n=6, p=0.59 and q=0.41 and the x=0, 1,2,3,4,5,6 but I am confused on how to get P(0)=0.005, P(1)=0.041, etc, etc. what is the most straightforward way to compute this.

Look at the expression for binomial distribution carefully. You will see:

P(n) = C(N,n) * p^n * q^(N-n)

I am having trouble with the Binomial Probability Formula:

in this example where p=0.25, q=0.75 and n=7 x=0,1,2,3,4,5,6,7
P(2)=21(0.25)^2 (0.75)^5=0.3115 (the ^ sybolizes the exponent here)

Where do they get the (21) that they multiply here?

C(7,2) = 21

Thanks
Peggy
Click to expand...
 
C(7,2) = 21

O.k. I apologize for my ineptness here but what is C? and then do you multipy C by 7 and then 2? This is what I don't get? Sorry
 
By definition:

\(\displaystyle C(N,n) \, = \, \frac{N!}{n!(N-n)!}\)

This is same as the number of ways you can choose 'n' subjects out of 'N' subjects (n<=N)
 
This is same as the number of ways you can choose 'n' subjects out of 'N' subjects (n<=N)

Again--sorry but can you show me this with the numbers in there so I can see exactly how to get 21?
 
peggyskold said:
This is same as the number of ways you can choose 'n' subjects out of 'N' subjects (n<=N)

Again--sorry but can you show me this with the numbers in there so I can see exactly how to get 21?
Click to expand...

Did you do problem like this:

You have 7 books with different titles. How many ways can you choose 2 books out of the group of 7?
 
I am not sure anymore--was just hoping I could see in this example where n=7 , P=0.25 andn q=0.75 and when asked P(2) how exactly I end up with 0.3115 because I don't get this?
 
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