--%>

Probability on expected number of days

It doesn't rain often in Tucson. Yet, when it does, I want to be prepared. I have 2 umbrellas at home and 1 umbrella in my office. Before I leave my house, I check if it is raining. If it is, I take one of the umbrellas with me to work, where I would leave it. When I go back home, I check if it is raining. If it is, I take one of the umbrellas with me home; therefore, the number of umbrellas at my house and in my office changes with time. The probability of rain is 0.1 every time I leave either my office or my house. The event of rain is independent of location and what happened in the past. Find the expected number of days before I run out of umbrellas where I am and it is raining outside. Also find the probability that I am home when that happens.

E

Expert

Verified

The person has 2 umbrellas at home and 1 in office. Also the probability of raining is independent of other factors and is equal to 0.1.

Now let us find the probability distribution of
X: Number of days before he running out of umbrellas.

Now X can take values from 0,1,2,3,..

Let us find the probability X=0, Now since he have 2 umbrellas at home and one at office, this probability will be zero.

Now let us find the probability x=1, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

When he will go office there is no rain, so probability is 0.9, now on returning there is rain with prob 0.1 now on second day leaving office there is no raining with 0.9 and at the time of return it rains with 0.1

Hence total probability is .9*.1*.9*.1

Now let us find the probability x=2, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

This probability will be .1*.9*.1*.9*.1  (The probabilities are arranged according to event)
Now let us find the probability x=3, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

The probability is .9*.1*.1*.1*.9*.1

The probability that more x ≥ 4 will be 1 minus all these probabilities

1053_probability.jpg

Hence the expected number of days is 3.97,

Means on an average more than 3 days required to run without umbrella.

   Related Questions in Advanced Statistics

  • Q : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer

  • Q : Grouped Frequency Distributions Grouped

    Grouped Frequency Distributions: Guidelines for classes: A) There must be between 5 to 20 classes. B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals. C) The classes should be mutually exclusive. This signifies that no data valu

  • Q : Probability of Rolling die problem A

    A fair die is rolled (independently) 12 times. (a) Let X denote the total number of 1’s in 12 rolls. Find the expected value and variance of X. (b) Determine the probability of obtaining e

  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

  • Q : Discrete and continuous data

    Distinguish between discrete and continuous data in brief.

  • Q : Problem on utility funtion probability

    Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.  Suppose further that you do not know whether or not you

  • Q : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

  • Q : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

  • Q : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.