Probabilities questions

Hey guys,

could anyone explain to me this question?

Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week, respectively?

A. A positive value; zero.
B. A positive value; infinite.
C. Zero; infinite.

The answer is B.

The answer should be A.

You can answer this question without any information whatsoever about the probability distribution; answers B and C are wrong for any probability distribution.

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Would you pls elaborate on that?
Does it relate to properties of probabilty?

Yes.

What are the properties of a probability function?

this sample problem is so terrible - it doesn’t teach you anything - that if you got this from a manual, i would consider asking for a refund.

  • 0 ≤ P(E) ≤1: the probability of any event E is a number between 0 and 1. The probability of 0 means that the event can never happen and the probability of 1 means that the event is certain to happen.
  • The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1.

The answer A is not obvious for me.

QBank Schweser

how many days are between those dates, inclusive?
answer that and you answered the question.

Now . . . look at answers B & C.

Spot on!

Well, you meant that for the option “the probability of it being sunny on 5 days” the probability is 1, which is positive?

As for the option “the probability of it being sunny on 10 days during the week” is zero as it is excluded from the period given?

I thought it requres a calculation of the binominal probability function.

It likely isn’t 1.

Are you looking at answers B & C?

B. A positive value; infinite.
C. Zero; infinite.

Based on the properties of the probability, the outcome can’t be infinitive?

Correct.

∞ > 1
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Thank you!

My pleasure.

Bill’s method is the fastest, but if you want to see that A is indeed correct:

The first part asks for the probability that are days of sun from April 20 to April 26. That’s a time period of 7 days. Clearly 7 days > 5 days, which means it’s possible that there could be 5 sunny days.
You are also given that p(x) = 0 when x cannot occur, or p(x) > 0 if it can.
Since this outcome is possible, it must have positive probability.

For the second part, you are asked the same thing, but instead of 5 days, you are given 10 days.
Clearly, 10 days can’t fit in a time period of 7 days, so the outcome is not possible.
You are given that p(x) = 0 when x cannot occur, or p(x) > 0 if it can.
Since the outcome can’t happen, the probability is zero.

Hence, A.

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Thank you for a fast and detailed response!

you’re very welcome :slight_smile: