Question

In: Math

5. Some state lotteries have a pick 3 game, where you can choose any number from...

5. Some state lotteries have a pick 3 game, where you can choose any number from 000 to 999. The state picks the winning number at random.
a) How many possible numbers can you choose from?
b) If all 3-digit numbers is equally likely what is the probability of any 1 specific number exactly matches the winning number?
c) Suppose you pick number 156 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?
d) Suppose you pick the number 111 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

Solutions

Expert Solution

a) How many possible numbers can you choose from?

- The range is 000-999. Thus, there are total 1000 possible number to choose (Each digit can be selected in 10 ways and 3 such digits can be selected in 10^3 = 1000 ways)

b) If all 3-digit numbers is equally likely what is the probability of any 1 specific number exactly matches the winning number?

- If all 3-digit numbers are equally likely then, P(1 specific number exactly matches the winning number) = 1/1000 = 0.001

c) Suppose you pick number 156 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

- If order doesn't matter then these three digits can be arranged in 3! ways = 6 ways

And total events possible are 100

Thus, required probability = 6/1000 = 0.006

d) Suppose you pick the number 111 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?

- Even though it is mentioned order doesn't matter, 111 can be selected only in 1 way

Thus. required probability = 1/1000 = 0.001


Related Solutions

There are two players in the game. Each player can pick any integer number between 1...
There are two players in the game. Each player can pick any integer number between 1 and n. If two numbers are the same then player 1 pays 1 dollar to player 2. If two numbers are different than nothing happens. (a) Prove that there are no equilibria in pure strategies; (b) Prove that in the equilibrium each strategy should be played with a positive probability. (c) Find all NE of the game.
The payoff X of a lottery ticket in the Tri-State Pick 3 game is $500 with...
The payoff X of a lottery ticket in the Tri-State Pick 3 game is $500 with probability 1/1000 and $0 the rest of the time. Assume the payoffs X and Y are for separate days and are independent from each other. a. What price should Tri-State charge for a lottery ticket so that they can break even in the long run (average profit =$ 0). b. Find the mean and standard deviation of the total payoff X+Y.
A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?
A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?
You have won a competition , and can choose any one of the following prize: a....
You have won a competition , and can choose any one of the following prize: a. 100,000 now b. 180,000 at the end of give of five years from c. 11,400 forever d. 19,000for each of the 10 years e . 6,500next year, and increaseing by 5% per year forever after If the interest rate is 12% what do you choose?
You have no health insurance and you are unemployed. Where can you go in your state(Texas),...
You have no health insurance and you are unemployed. Where can you go in your state(Texas), county(Liberty), or city(Cleveland) for medical services?
Suppose you choose a coin at random from an urn with 3 coins, where coin i...
Suppose you choose a coin at random from an urn with 3 coins, where coin i has P(H) = i/4. What is the pmf for your prior distribution of the probability of heads for the chosen coin? What is your posterior given 1 head in 1 flip? 2 heads in 2 flips? 10 heads in 10 flips?Hint: Compute the odds for each coin first.
Write a game where a user has to guess a number from 1 – 6, inclusive....
Write a game where a user has to guess a number from 1 – 6, inclusive. Your program will generate a random number once (pick a number), and will then prompts the user to guess the number for up to 3 times. If the user enters 3 wrong guesses, the program should be terminated along with the losing message. Once the user has successfully guessed the number, tell the user they win, and tell them how many guesses it took...
Why do you think that some religious people pick and choose the doctrines to follow while...
Why do you think that some religious people pick and choose the doctrines to follow while ignoring others that are written out in their scriptures?
In the ground state of atomic hydrogen the electron can be pictured as existing some- where...
In the ground state of atomic hydrogen the electron can be pictured as existing some- where within a distance ∆x from the position of the nucleus with ∆x interpreted as the uncertainty in the position of the electron. (a) If ∆x is taken ot be the Bohr radius, calculate the uncertainty in the momentum of the electron. (b) If the uncertainty relation is written as rp = h(bar)?, the energy of the hydrogen atom can be expressed by E(p)=(p^2/2m)-(e^2p/h) Calculate...
For the project: You will have to choose any product. You are the managerial accountant and...
For the project: You will have to choose any product. You are the managerial accountant and you will have to estimate its cost. In so doing, try to give examples about the several costs incurred (manufacturing and nonmaufacturing) and use what you have learned in this course to be able to know the cost of your product. For your chosen product you may want to address the following costs incurred (note that what you may want to provide is NOT...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT