[MERGED] Probability and Probability Distributions

[cass333]

I was hoping someone could help me get started with this homework question... Stats is really difficult for me so the easiest problems take me forever to figure out.

The utility company in a large metropolitan area finds that 70% of all its customers pay a given monthly bill in full.
a. Suppose two customers are chosen at random from the list of all customers. What is the probability that both customers will pay their monthly bill in full?

I just need to figure out what to set A and B as and what formula to use? I was assuming since it says "both" that I would be using the intersection of event A and B. But when I try to figure out what A and B could be, nothing makes sense logically to me. Any help would be greatly appreciated!

Thanks so much,
Cassie

 

[Mrspi]

Re: Probability and Probability Distributions

I was hoping someone could help me get started with this homework question... Stats is really difficult for me so the easiest problems take me forever to figure out.

The utility company in a large metropolitan area finds that 70% of all its customers pay a given monthly bill in full.
a. Suppose two customers are chosen at random from the list of all customers. What is the probability that both customers will pay their monthly bill in full?

I just need to figure out what to set A and B as and what formula to use? I was assuming since it says "both" that I would be using the intersection of event A and B. But when I try to figure out what A and B could be, nothing makes sense logically to me. Any help would be greatly appreciated!

Thanks so much,
Cassie

If 70% of the customers pay their bill in full, then the probability that any particular customer pays his/her bill in full is 0.7.

If you pick two customers at random, whether or not they pay their bills in full is independent...that is, the first customer's bill paying has no effect whatsoever on the second customer's bill paying.

So, P(first customer pays bill AND second customer pays bill) = P(first customer pays bill)*P(second customer pays bill)

So, P(first customer pays bill AND second customer pays bill) = 0.7*0.7

 

[cass333]

Re: Probability and Probability Distributions

Thanks so much... I knew it was going to be something super simple. I was probably just making it more complicated than it needed to be. I really appreciate your help!

 

[tkhunny]

Re: Probability and Probability Distributions

Have you met the Binomial Distribution? Very, very important.

Remember this from algebra? (a+b)^2 = a^2 + 2ab + b^2

If we assign a = 70% - the probability of a full bill payer, we have
b = 30% - the probability of a partial bill payer.

This gives:

(a+b)^2 = 0.7^2 + 2(0.7)(0.3) + (0.3)^2

OR

P(Both are full bill payers) = 0.7^2
P(Both are partial payers) = 0.3^2
P(One of each) = You tell me.

Now answer the question.