New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six...

New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. (a) Do calculations for winning this lottery involve permutations or combinations? why? (b) How many different lottery tickets are possible? (c) Find the probability of winning the jackpot when one ticket is purchased?

Solutions

Expert Solution

Solution:

Permutations of objects are the arrangements of the objects. In the arrangement, order of objects matters.

For example if we have three objects M, N, O, there are total 6 arrangements of objects are possible MNO, MON, OMN, NMO, NOM, ONM. Total number of permutation of r objects out of n objects is denoted by P and given by

Combination is the selection of r objects out of n different objects and order of the selection of objects does not matter. If there are 3 objects A, B and C and we have to select 2 objects out of three. Then selection AB and BA are same. Total number of combinations of objects out of n objects is denoted nCr by and given by

Since here order of selection of 6 numbers out of 49 numbers does not matter so combination should be used.

Hence, calculations for winning lottery involve combination

Please post remaining as new question... Please

orchestra answered 1 year ago

Next > < Previous

Related Solutions

New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six...

New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. b) How many different lottery tickets are possible? (c) Find the probability of winning the jackpot when one ticket is purchased?

A typical "Pick Six" lottery run by some states and countries works as follows: Six numbered...

A typical "Pick Six" lottery run by some states and countries works as follows: Six numbered balls are selected (unordered, without replacement) from 49. A player selects at random six balls. Calculate the following probabilities: a. The player matches exactly three of the six selected balls. b. The player matches exactly four of the six selected balls. c. The player matches exactly five of the six selected balls. d. The player matches exactly six of the six selected balls.

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.

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick...

Let’s suppose that you are going to play the lottery game Powerball. To play, you pick five different numbers from 1 through 69 plus one Powerball number from 1 through 26. Which is a more likely combination of winning numbers: 1, 2, 3, 4, 5, 6 or 7, 21, 25, 32, 40, 56? Explain your answer. For a $500,000,000 jackpot, which of the two combinations would likely be more lucrative for you if it were to win? In other words,...

In the lottery of a certain state, players pick six different integers between 1 and 49,...

In the lottery of a certain state, players pick six different integers between 1 and 49, the order of the selection being irrelevant. The lottery commission then selects six of these numbers at random as the winning numbers. A player wins the grand prize of $1,200,000 if all six numbers that he has selected match the winning numbers. He wins the second and third prizes of $800 and $35 respectively, if exactly five and four of his six selected numbers...

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the...

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $1,100 at the end of January, $2,400 at the end of February, $3,700 at the end of March, and so on up to $15,400 at the end of December. At the beginning of the next year, the sequence repeats starting at $1,100 in January and ending at $15,400 in December. This annual sequence of payments repeats indefinitely. If the...

A state is starting a lottery game. To enter this lottery, a player uses a machine...

A state is starting a lottery game. To enter this lottery, a player uses a machine that randomly selects six distinct numbers from among the first 30 positive integers. The lottery randomly selects six distinct numbers from the same 30 positive integers. A winning entry must match the same set of six numbers that the lottery selected. The entry fee is 1, each winning entry receives a prize amount of 500,000, and all other entries receive no prize. Calculate the...

Consider the discrete Bertrand game. According to the rules of this game each student selects a...

Consider the discrete Bertrand game. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game? Explain your reasoning.

1.According to the Port Authority of New York and New Jersey, 81.9% of New Jersey Transit...

1.According to the Port Authority of New York and New Jersey, 81.9% of New Jersey Transit trains ran on time during 2018. Assume that this percentage still holds true. Using the normal approximation to the binomial distribution, determine the probability that the next 30 trains a. a. Fewer than 22 trains will run on time b. b.Exactly 26 trains will run on time c. c. 21,22,23, or 24 will run on time. 2. Consider that the hits on the Amazon website follow the exponential distribution...

The Arizona pick 6 "Lotto" lottery says you're a winner if your letter ticket has 3,4,5,...

The Arizona pick 6 "Lotto" lottery says you're a winner if your letter ticket has 3,4,5, or 6 of the winning numbers (of 42 to choose from). If you buy one lottery ticket, what is the probability that your ticket is a loser? PLEASE explain and show how you did this step by step. IM TRYING to actually learn how to do this problem.

Subjects