What is the probability of losing at the first toss

Assignment Help Basic Statistics
Reference no: EM13965102

Homework

Be sure to state what probability distribution you assume in each problem! You may find the necessary probabilities in tables, compute them manually with a calculator, or use computer software.

PART I

In preparation for a game of "Craps", you were asked the following questions:

a. What is the probability of winning at the first toss of the dice?

b. What is the probability of losing at the first toss?

c. If the first toss is 4, what is the probability of winning on the next toss?

d. What is the probability of throwing a "7 or 11" at least twice in six throws of a standard pair of dice?

e. What is the expected number of 7's & 11's obtained in 6 throws of a pair of dice?

f. What is the expected number of throws of a pair of dice required in order to obtain a 7 or 11?

g. Obtain a pair of dice and throw them six times. How many times did you throw "7 or 11"?

Here are the basic rules of craps. A die is a cube with the faces numbered in such a way that the opposite faces sum to 7, e.g., 3 & 4 are opposite, 1 & 6 are opposite, 2 & 5 are opposite. In the game of "craps", two dice are rolled, and the sum of their uppermost faces is observed.

Win

Lose

Roll a 7 or 11 on the first roll,

Roll a 2, 3, or 12 on the first roll,

- or -

- or -

Roll a 4, 5, 6, 8, 9, or 10,

Roll a 4, 5, 6, 8, 9, or 10,

and roll the original number again

and then a 7 before you roll the

before a 7 comes up

original number again

That is, if the sum has value 2, 3, or 12, the player loses immediately. If the sum is 7 or 11, the player wins. Otherwise (if the sum is 4, 5, 6, 8, 9, or 10) further rolls are required to resolve the game. If, for example, the first sum is 5, then the dice are rolled repeatedly until either a sum of 5 reappears (in which case the player wins) or a sum of 7 appears (in which case the player loses.)

PART II

The foreman of a casting section in a certain factory finds that on the average, 1 in every 9 castings that are made is defective.

a. If the section makes 15 castings a day, what is the probability that 2 of these will be defective?

b. If the section makes 15 castings a day, what is the probability that 3 or more defective castings are made in one day?

c. If the section makes 8 castings a day, what is the probability that 2 or less defective castings are obtained?

PART III

Along highway I-25 in Las Cruces, the probability that each passing car stops to pick up a hitchhiker is p=4%, i.e., an average of one in twenty-five drivers will stop; different drivers, of course, make their decisions to stop or not independently of each other.

a. Each car may be considered as a "trial" in a process, with "success" defined as the car's stopping to pick up the hitchhiker.

b. Given that a hitchhiker has counted 15 cars passing him without stopping, what is the probability that he will be picked up by the 25th car or before?

Suppose that the cars arrive according to a Poisson process, at the average rate of 15 per minute. Then "success" for the hitchhiker occurs at time t provided that both an arrival occurs at t and that car stops to pick him up. Let T1 be the time (in seconds) of the first "success", i.e., the time that he finally gets a ride, when he begins his wait at time t = 0.

c. What is the arrival rate of "successes"?

d. What is the name of the probability distribution of T1?

e. What is the value of E(T1) ? What's the value of Var(T1)?

f. What is the probability that he must wait less than 2 minutes for a ride (P{T1< 2}?

g. What is the probability that he must wait more than 2 minutes for a ride (P{T1> 2}?

h. What is the probability that he must wait exactly 2 minutes for a ride (P{T1= 2}?

Suppose that after 2 minutes (during which 28 cars have passed by) the hitchhiker is still there waiting for a ride.

i. What is the conditional expected value of T1 (expected total waiting time, given that he has already waited 2 minutes)?

Part IV: Adding a profile picture and short biography

Please add a profile picture and short biography to the class Canvas website. Your profile picture has to be acceptable for facial recognition purposes.

Reference no: EM13965102

What is the average rating for all cbc movies

What is the average rating for all CBC movies and How about ABN movies and BBS movies - What is your recommendation to the executives? Justify your answer referring to the rel

What is the probability that will get a raise?

Consider that you are a line manager in your current Corporation. There is a0.50 probability that you will be promoted this year. There is a 0.65 probability thatyou will get

Provide arguments supporting this result

Compute the mean μFM and variance σ2 FM under the null hypothesis H0: ? = 0 for the Fligner- MacEachern statistic FM (15.37) presented in Comment 19. What is the asymptotic

Create a histogram of the time until first failure

Create a histogram of the time until first failure for this type of disc player.- Then find a 95% confidence interval for the mean time until failure for this type of disc pla

National cancer-incidence rates

Twelve cases of leukemia are reported in people living in a particular census tract over a 5-year period. Is this number of cases abnormal if only 6.7 cases would be expecte

Information regarding rules of probability

A manager of a gasoline filling station is thinking about a promotion that she hopes will bring in more business to the full-service island. She is considering the option th

Determine the mean and the standard deviation

a. Determine the mean and the standard deviation of x. b. For the sample size n 5 2, determine the mean for each possible simple random sample from this population. c. For eac

Problem regarding the poisson random variable

1. A fair coin is tossed 10 times. Let X denote the number of heads obtained. Find the following. 2. Let X be a Poisson random variable with λ = 1/3. Find

Reviews

Write a Review

 
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd