HELP A Certain state's lottery LOTTO, is set up so that each player pays $1 per ticket and chooses six different numbers from 1 to 49. if the six numbers chosen match the six numbers drawn each Saturday evening, the player wins the top cash prize. the order in which the numbers are drawn does not matter
a) if a person buys 1 lottery, what is probability of winning grand prize
b) if he buys 10,000 tickets, what is probability of winning grand prize
c) how much must a person spend so that his probability of winning is 1/2
d) what are the odds against winning the lottery in this state, assuming that only 1 ticket is purchased
e) if the grand prize is $1,000,000 and there is only one winner, find a player expected value if he purchase 1 ticket (assume all tickets have been sold, all combination have been chosen, and there are no duplicate tickets
f) what states do not have a lottery?
please answer what you can and help
a) prob winning = 1/C(49,6) = 1/13,983,816
b) 10,000/13,983,816
c) x/13,983,816 = 1/2 , solve for x
d) prob not winning = 13,983,815/13,983,816
odds against winning = 13,983,815 : 13,983,816
e) expected value = 1,000,000(prob of a) )
Thanks, Reiny I see you answer a lot of questions for people. Thank you for taking the time out to help others that struggle in math. Your help is greatly appreciated
a) To find the probability of winning the grand prize with one ticket, we need to determine the number of ways to win and divide it by the total number of possible outcomes. In this case, there is only one winning combination (6 numbers match) out of a total of C(49,6) possible combinations. The notation "C(n,r)" represents the number of combinations of r items chosen from a set of n items.
So, the probability of winning with one ticket is:
1 / C(49,6) = 1 / 13,983,816
b) To find the probability of winning the grand prize with 10,000 tickets, we can simply multiply the probability of winning with one ticket by the number of tickets purchased:
P(10,000 tickets) = P(1 ticket) * 10,000
c) To calculate the amount a person must spend to have a probability of winning of 1/2, we need to find the number of tickets that would result in this probability:
P(number of tickets) = 1 / 2
P(number of tickets) = P(1 ticket) * number of tickets
Solving the equation, we get:
1 / 2 = 1 / 13,983,816 * number of tickets
number of tickets = (1 / 2) * 13,983,816 ≈ 6,991,908
Therefore, a person must spend approximately 6,991,908 dollars to have a probability of winning of 1/2.
d) The odds against winning the lottery can be calculated by taking the ratio of unfavorable outcomes to favorable outcomes. In this case, there is only one winning combination out of C(49,6) possible combinations.
So, the odds against winning the lottery with one ticket are: (C(49,6) - 1) : 1
e) The expected value is the average amount you can expect to win or lose per ticket. To calculate the expected value, we need to consider the probability of winning and the prize amount.
The probability of winning with one ticket is 1 / C(49,6), as calculated before. The prize amount is $1,000,000.
Expected Value = (Probability of Winning * Prize Amount) - Ticket Cost
Expected Value = (1 / C(49,6)) * $1,000,000 - $1
f) As an AI, I don't have real-time information on the current status of lotteries in different states. However, as of my knowledge, in 2021, the states without a lottery are Alabama, Alaska, Hawaii, Mississippi, Nevada, and Utah. Please note that this information might change over time, so it's advisable to check with reliable sources for the most up-to-date information.