2. A box contains three fair coins, and two trick coins that have heads on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is the probability that it's one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?

2. A box contains three fair coins, and two trick coins that have heads on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is the probability that it's one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.4: Bayes’ Rule

Problem 1P

See similar textbooks

Similar questions

Suppose for an international football tournament, you wish to find the probability of the country who can win the final game. You can find the odds for winning from your local bookie [A bookie sets odds, accepts and places bets, and pays out winnings on behalf of other people]. Odds are mathematically treated as a fraction. If the odds for the Morocco vs Argentina game are 5 to 1, the fraction is 1 / 5. So to convert the fraction into probability of winning, take the numerator and divide it by the denominator plus 1. Use the Frac.class in Java to help you convert any given odds into probability. Display your result as a percentage on you console.
A coin is flipped 10 times in a row. a. What is the probability that it lands heads up exactly 8 times? b. What is the probability that it lands heads up at least 8 times? c. What is the probability that it lands heads up at most 8 times
There are three financial aid counselors. If a student’s last initial is from A – H, let them know that their counselor is Jon Stewart. If a student’s last initial is from I – Q, let them know that their counselor is Chelsea Handler. If a student’s last initial is from R – Z, let them know that their counselor is Brian Williams.Ask student for the FICO score, if it’s less than 660 tell that this student cannot have a loan.
One day, an elf jumps out at you from behind a garbage can and proposes a wager. He says that if the weather in Leipzig, Germany tomorrow is sunny, he'll give you $20, if it's cloudy (but dry) he'll give you $1, but if neither of those are the case you owe him $15. Helpfully, he also provides you data that indicates that the probability of sunny weather in Leipzig tomorrow is 40% and cloudy-but-dry is 10%. How much do you expect to win or lose from this wager (if you accept it)? A)Win $15.60 B)Lose $6.00C)Lose $7.50D)Win $0.60E)Win $4.00
EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)
A proposition Q follows from a proposition P, if Q is never false when P is true. Suppose we want to check this in a particular case. Which of the following is correct? Select one: a. We need to check that whenever P is false, Q is also false. b. We need to check that whenever Q is false, P is also false. c. We need to check that whenever Q is true, P is also true. d. We need to check that Q is true when P is true, and that Q is false when P is false.
Suppose a person can buy a chocolate bar from the vending machine for $1 each. Inside every chocolate bar is a coupon. A person can redeem 3 coupons for one chocolate bar from the machine. This means that once a person has started buying chocolate bars from the machine, he/she always has some coupons. A person would like to know how many chocolate bars can be bought, if a person starts with N dollars and always redeem coupons, if he/she has enough for an additional chocolate bar. For example: With 3 dollars a person could buy 4 chocolate bars after purchasing 3 bars giving him/her 3 coupons and then redeeming the 3 coupons for one bar. This would leave him/her with one extra coupon. Thus, will have 4 chocolate bars and still have one coupon leftover. For 11 dollars, a person can have 16 chocolate bars and still have one coupon leftover. For 12 dollars, a person can have 17 chocolate bars and have two coupons leftover. Write a complete Python program that prompts a buyer to input…
The bean machine, also known as a quincunx or the Galton box, is a device for statistics experiments named after English scientist Sir Francis Galton. It consists of an upright board with evenly spaced nails (or pegs) in a triangular pattern, as shown in Figure 10.15. Balls are dropped from the opening of the board. Every time a ball hits a nail, it has a 50% chance of falling to the left or to the right. The piles of balls are accumulated in the slots at the bottom of the board. Write a program that simulates the bean machine. Your program shouldprompt the user to enter the number of the balls and the number of the slots in the machine. Simulate the falling of each ball by printing its path. For example, the path for the ball in Figure 10.15b is LLRRLLR and the path for the ball in Figure 10.15c is RLRRLRR. Display the final buildup of the balls in the slots in a histogram.
The next two questions refer to the following belief network with random variablesF0,F1,…,F4 which only take the values 0 and 1. Which of the following statements are true about this belief network (1), (3) and (4) only :(1) F0 and F3 are independent given F1,F2 ;(2) F0 and F2 are independent;(3) P(F0∣F1,F2)=P(F0∣F1,F2,F3,F4) ;(4) F0 and F4 are independent. In general, to define the joint probability distribution P(F0,…,F4) one requires up to 25−1 entries in the table of probabilities. For the belief network above, one can compute the joint probability distribution P(F0,…,F4) using the following number of conditional probabilities
Given that A and B are real variables with values 1.5, and 2.5respectively, and C is integer variable with value 3, evaluate thefollowing: NOT(A<0) AND (B/C<=0).
Down_and_distance Run Pass1st_down_and_10_or_more_yards_to_go 56 802nd_down_and_6_or_more_years_to_go 27 522nd_down_and_5_or_less_yards_to_go 19 93rd_down_and_2_or_more_yards_to_go 4 603rd_down_and_1_yard_to_go 1 4 a) What is the probability that the team will pass the ball on any given down? enter your response here (Round to three decimal places as needed.) Part 2 b) What is the probability that the team will run the ball and it is second down? enter your response here (Round to three decimal places as needed.) Part 3 c) What is the probability that the team will pass the ball, given that it is 3rd down and they have 1 yard to go? enter your response here (Round to three decimal places as needed.) Part 4 d) What is the probability that the team will run the ball and it is 1st down? enter your response here (Round to three decimal places as needed.) Part 5 e) What is the probability that the team will run the ball,…
We are given the following: D = set of all students at your school M(s) = “s is a math major” C(s) = “s is a computer science student” E(s) = “s is an engineering student” Use quantifiers, variables, and the predicates M(s), C(s), and E(s) to express the statement of “Some computer science students are also math majors”