A certain state's lottery game, LOTTO, is set up so that each player pays $1 per ticket and chooses six different numbers between 1 and 20 inclusive. If the six numbers chosen match the six numbers drawn, the player wins the grand prize.
If a person buys one LOTTO ticket, what is his probability of winning the grand price?
20 x 20 x 20 x 20 x 20 x 20
You have 20 chances for each number and that happens for each draw...
you have 1 chance out of _________
Can you finish from here?
Joe has assumed that the same number could be drawn more than once.
However,in most of these lotteries, some kind of drawing method is used, such as 20 different-numbered pingpong balls, and the order that they are drawn does not matter.
Number of ways to draw 6 numbers from 20
is C(20,6) = 38760
so prob(winner) = 1/38760
Thank You, Joe and Reiny for your help. I believe Reiny you use combination formula and I believe you are right, because the question does states that the order doesn't matter. Once again thanks to you both
I decided to add my name. This is my first time on here and I wanted to see what its all about...
another question I'm struggling with
If a person buys 1000 LOTTO tickets, what is his probability of winning the grand prize?
Assuming that you don't play the same set of numbers and it is the same drawing. All you do is add the number of tickets bought to the top number so 1000/38760. Which is about a 2.5% chance of winning. If it is one ticket a game for a 1000 times. It stays 1/38760.
To find the probability of winning the grand prize in the LOTTO game, we need to determine the number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the total number of ways to choose 6 numbers from 20. This can be calculated using the combination formula.
The formula for combination is:
C(n, r) = n! / (r! * (n-r)!), where n is the total number of items to choose from, and r is the number of items to choose.
In the LOTTO game, n = 20 (the total number of available numbers) and r = 6 (the number of numbers chosen).
Using this formula, we can calculate the total number of possible outcomes:
C(20, 6) = 20! / (6! * (20-6)!)
= 20! / (6! * 14!)
= (20 * 19 * 18 * 17 * 16 * 15) / (6 * 5 * 4 * 3 * 2 * 1)
= 38,760
So, there are 38,760 possible outcomes in the LOTTO game.
Next, we need to determine the number of favorable outcomes, which is the number of ways to choose 6 numbers that match the 6 numbers drawn. Since there is only one winning combination, the number of favorable outcomes is 1.
Now we can calculate the probability of winning the grand prize:
Probability = Number of favorable outcomes / Number of possible outcomes
= 1 / 38,760
The probability of winning the grand prize in the LOTTO game with one ticket is approximately 0.0000258, or about 0.003%.
Please note that winning probabilities and prize amounts may vary depending on the specific rules and regulations of the LOTTO game in a certain state or country.