What Are the Chances of Water Rationing Over a Decade in Southland?

[vipertongn]

Water shortages require water rationing policies. From past records, we know that the probability that water needs to be rationed in a southland water district in any given year is 0.15. Assume that water rationing in consecutive years are independent events.

Let X be the number of years with water rationing in a sample of ten years. What is the expected (mean) number of years with water rationing in 10 years for a southland water district?
For this one E(X)=np=1.5 i think

What is the probability that there would be no water rationing in the next ten years?

I'm not sure how to calculate this...i know at least for one year it should be .85 is that right?

What is the probability that there would be water rationing in at least two of the next ten years?
I'm assuming this would be 2*.15

 

[LCKurtz]

Water shortages require water rationing policies. From past records, we know that the probability that water needs to be rationed in a southland water district in any given year is 0.15. Assume that water rationing in consecutive years are independent events.

Let X be the number of years with water rationing in a sample of ten years. What is the expected (mean) number of years with water rationing in 10 years for a southland water district?
For this one E(X)=np=1.5 i think

Yes. Do you recognize a binomial distribution here?

What is the probability that there would be no water rationing in the next ten years?

I'm not sure how to calculate this...i know at least for one year it should be .85 is that right?

Yes.

What is the probability that there would be water rationing in at least two of the next ten years?
I'm assuming this would be 2*.15

No. What is the probability for (A AND B) if A and B are independent?

 

[vipertongn]

I hate to bring up an old thread, but I'm reviewing this and i haven't gotten the answer for the last two really.
What is the probability that there would be no water rationing in the next ten years?
ok, I think for this case I calculate it first the probability of it actually not occurring, which is...
P(X=0)= 10C0*p^0(0.85)^10= 0.197

Which I hope is correct...

Then for the next one I calculate the probabilities of it occurring at LEAST 2 times by finding the probabilities of 1 and 2 happening and then adding them with the .197
P(X=1)=.35
P(X=2)=.27
so it would become about .83. For it to at least be occurring 1-.83 = .17 of 2 rationings occurring

I hope I'm correct

 

[LCKurtz]

I hate to bring up an old thread, but I'm reviewing this and i haven't gotten the answer for the last two really.
What is the probability that there would be no water rationing in the next ten years?
ok, I think for this case I calculate it first the probability of it actually not occurring, which is...
P(X=0)= 10C0*p^0(0.85)^10= 0.197

Which I hope is correct...

Yes.

Then for the next one I calculate the probabilities of it occurring at LEAST 2 times by finding the probabilities of 1 and 2 happening and then adding them with the .197
P(X=1)=.35
P(X=2)=.27
so it would become about .83. For it to at least be occurring 1-.83 = .17 of 2 rationings occurring

I hope I'm correct

No. The complementary event to "at least two" is "zero or one". You just need to subtract the probabilities for 0 and 1.