Lottery One state lottery game has contestants select 5 different numbers from 1 to 45. The prize if all numbers are matched is 2 million dollars. The tickets are $2 each. 1) How many different ticket possibilities are there? 2) If a person purchases one ticket, what is the probability of winning? What is the probability of losing? 3) Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets. a) How much would each person have to contribute? b) What is the probability of the group winning? Losing? 4) How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it? 5) Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket. 6) In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games. Find the expected value of x = the amount won/lost when purchasing one ticket.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Lottery
One state lottery game has contestants select 5 different numbers from 1 to 45. The prize if all numbers are matched is 2 million dollars. The tickets are $2 each.
1) How many different ticket possibilities are there?
2) If a person purchases one ticket, what is the
3) Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets.
a) How much would each person have to contribute?
b) What is the probability of the group winning? Losing?
4) How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?
5) Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.
6) In fair games, the
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
