expected value

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins? Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins Expected Value of...

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are expected to be spies? Expected Spies = Probability of being a spy * Total Soldiers Expected Spies = 0.0005 * 10000 Expected Spies = 5

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find the expected value. Expected Value E(x) is: E(x) = Probability of winning * Winning Price - Probability of losing * Ticket Price Since only 1 cash price will be given, 2299 will be losers: E(x) =...

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6 Expected Value = Rolls * Probability Since a 6 has a probability of 1/6, we have: Expected Value = 300 * 1/6 Expected Value = 50

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5. Set up the expected values E(x): for the 1,000 price: E(x) = (1000 - 5) * 1/1000 = 995/1000 For the 5 $100 prizes: E(x) = (100 - 5) * 5/1000 = 475/1000 For the...

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store. Calculate the expected...

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two...

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins? We want Expected Value of s spins. Set up the expected value formula for any number 1-4 E(s)...

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2] Multiply through E[(2Y + 1)^2] = E[4y^2 + 4y + 1] We can take the expected value of each term E[4y^2] + E[4y] + E[1] For the first term, we have: 4E[Y^2] We define the Var[Y] = E[Y^2] - (E[Y])^2 Rearrange this term, we have E[Y^2] = Var[Y]...

Imagine you are in a game show. Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning (a) What is your expected winning in this...