--%>
Assignment Help - homework help

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 : 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 : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : Problem on consumers marginal utility

    Consider a consumer with probability p of becoming sick.  Let Is be the consumer’s income if he becomes sick, and let Ins be his income if he does not become sick, with Is < Ins. Suppo

    		•
  • Q : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•
  • Q : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a

    		•
  • Q : Probability of signaling Quality

    Quality control: when the output of a production process is stable at an acceptable standard, it is said to be "in control?. Suppose that a production process has been in control for some time and that the proportion of defectives has been 0.5. as a means of monitorin

    		•
  • Q : Components of time series Name and

    Name and elaborate the four components of time series in brief.

    		•
  • 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 : Binomial distribution 1) A Discrete

    1) A Discrete random variable can be described as Binomial distribution if is satisfies four conditions, Briefly discuss each of these conditions2) A student does not study for a multiple choice examination and decides to guess the correct answers, If the

    		•