Question

In: Math

Suppose you have four extra tickets to a football game and you are trying to determine...

Suppose you have four extra tickets to a football game and you are trying to determine which of your five closest friends to take with you: Mark, Samuel, Elizabeth, James, and Mary. You decided to randomly choose four of them to attend the game with you. What is the probability that you will choose at least one friend whose name starts with the letter M? 0 2/5 4/5 1 2

Solutions

Expert Solution

Solution

Back-up Theory

Probability of an event E, denoted by P(E) = n/N ……………………………………....................................……........……(1)

where

n = n(E) = Number of outcomes/cases/possibilities favourable to the event E and

N = n(S) = Total number all possible outcomes/cases/possibilities.

Number of ways of selecting r things out of n things is given by nCr = (n!)/{(r!)(n - r)!}…...............................................…(2)

Values of nCr can be directly obtained using Excel Function: Math & Trig COMBIN…...............................................…. (2a)

Number of ways of selecting r things out of n things when p specific things must be selected is given by n - pCr - p....... (3a)

Number of ways of selecting r things out of n things when p specific things must NOT be selected is given by n - pCr....(3b)

Number of ways of selecting r things out of n things when p specific things must be selected and q specific things must NOT be selected is given by n – p - qCr - p................................................................................................................. (3c)

Now, to work out the solution,

Out of 5 names, two names, namely, Mark and Mary start with the letter M.

‘Choose at least one friend whose name starts with the letter M’ =>

Exactly one friend whose name starts with the letter M, i.e., Mark is selected but Mary is not selected

Or,

Both Mark and Mary are selected.

Vide (3c), number of selections for the first case is: 3C3 = 1

Vide (3a), number of selections for the second case is: 3C2 = 3.

So, there are 4 selections possible where at least one friend whose name starts with the letter M. Vide (1), n = 4

Vide (2), 4 out of 5 friends can be selected in 5C4 = 5 ways and vide (1), N = 5

Hence, vide (1), probability that you will choose at least one friend whose name starts with the letter M

= 4/5 Third Optiion Answer

DONE


Related Solutions

A university is trying to determine what price to charge for tickets to football games. At...
A university is trying to determine what price to charge for tickets to football games. At a price of ​$21 per​ ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $4.50 on concessions. What price per ticket should be charged in order to maximize​ revenue? How many people will attend at that​ price? What is the price per​ ticket? What is the...
A university is trying to determine what price to charge for tickets to football games. At...
A university is trying to determine what price to charge for tickets to football games. At a price of ​$27 per​ ticket, attendance averages 40,000 people per game. Every decrease of ​$33 adds 10,000 people to the average number. Every person at the game spends an average of ​$4.50 on concessions. What price per ticket should be charged in order to maximize​ revenue? How many people will attend at that​ price?
A university is trying to determine what PRICE to charge for football tickets. At a price...
A university is trying to determine what PRICE to charge for football tickets. At a price of $6 per ticket, it averages 70,000 people per game. For every increase of $1, it loses 10,000 people from the average number . Every person at the game spends an average of$1.50 on concessions. a) What price per ticket should be charged to MAXIMIZE REVENUE? ( Please explain the steps ) b) How many people will attend at that price? Please show your...
A university is trying to determine what price to charge for tickets to football games. At...
A university is trying to determine what price to charge for tickets to football games. At a price of ​$22 per​ ticket, attendance averages 40,000 people per game. Every decrease of ​$22 adds 10,000 people to the average number. Every person at the game spends an average of ​$3.00 on concessions. What price per ticket should be charged in order to maximize​ revenue? How many people will attend at that​ price?
Suppose the demand for tickets to a Titans' football game is given by the equation P...
Suppose the demand for tickets to a Titans' football game is given by the equation P = 200 - .002Qd. Total player costs are $40m, and the remaining costs of operating the franchise are $10m. All of the costs are fixed (let MC=0), and stadium capacity is 55,000. What is the profit maximizing price and quantity for Titans tickets? Depict your solution in a diagram. Be thorough and precise. Suppose the Titans signed better players. What would happen to ticket...
You have three tickets to a Celtics game on a night that you are going to...
You have three tickets to a Celtics game on a night that you are going to be out of town (so the value of unsold tickets is zero to you). There are only four possible buyers of a Celtics ticket. The table below lists the respective reservation prices of these four possible buyers: Customer Reservation Price 1 $25 2 $35 3 $50 4 $60 How much revenue can you generate if you charge a single price of $25 for the...
You are trying to determine te profit maximizing price for video game console. Currently you are...
You are trying to determine te profit maximizing price for video game console. Currently you are charging $180 and selling 2 million consoles per year. It costs $150 to produce a console, and price elasticity of demand for console is 3. What price should you charge for a console. Use excel solver to find the result and the graph.
In a football or soccer game, you have 22 players, from both teams, in the field....
In a football or soccer game, you have 22 players, from both teams, in the field. What is the probability of having any two players with the same birthday? (just assume 365 days a year and don’t have to do the exact calendar month and day, use the day number from 1 to 365) Find the closed form mathematical solution by probability theory. Show your derivation/proof.
Suppose you are trying to determine the number of boxes you need to order to be...
Suppose you are trying to determine the number of boxes you need to order to be able to ship the orders from your small business this week. You consistently over- or underestimate how many you need, so you decide to figure it out with statistics! You take a sample of data you’ve recorded from past orders. Consider a sample with the following properties: x̅ = 893.6, s = 63.2, n = 48 A) Why might you prefer an interval estimate...
Suppose you are trying to determine the capacity (in gallons) of the gas tank needed on...
Suppose you are trying to determine the capacity (in gallons) of the gas tank needed on an airplane you are constructing. You want to be able to travel 3200 nautical miles without stopping, and have gathered data on the amount of fuel similar planes used during flights of comparable length. Show complete calculation and your steps, also interpetation and explanation as asked. Consider a sample with the following properties: x̅ = 261.5, s = 18.73, n = 26 A) Calculate...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT