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?
As I stated in my previous reply to the same post ....
Number of ways to draw 6 numbers from 20
is C(20,6)
= 20!/(6!14!)
= 38760
so prob(winner) = 1/38760
Okay, but I was wondering would you use the same method (combination) for this question
If a person buys 1000 LOTTO tickets, what is his probability of winning the grand prize?
yes
if the prob of winning by buying 1 ticket is 1/38760
then the prob of winning with
1000 tickets is
= 1000(1/38760)
= 25/969
Thanks
To find the probability of winning the grand prize in the LOTTO game, we need to calculate the number of successful outcomes (matching all six numbers) divided by the total number of possible outcomes.
1. First, let's calculate the number of successful outcomes. Since the player must match all six numbers, there is only one combination of winning numbers.
Successful outcomes = 1
2. Now, let's calculate the total number of possible outcomes. The player chooses six different numbers between 1 and 20 inclusive. To calculate the total number of possible outcomes, we'll use the concept of combinations.
The formula for combinations is:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of options and r is the number of choices.
In this case, n = 20 (the total numbers to choose from) and r = 6 (the number of choices).
Total number of possible outcomes = C(20, 6) = 20! / (6! * (20-6)!)
Evaluating this expression, we find:
Total number of possible outcomes = 38,760
3. Finally, we can calculate the probability of winning the grand prize:
Probability = successful outcomes / total outcomes
= 1 / 38,760
Therefore, the probability of winning the grand prize in the LOTTO game, if a person buys one ticket, is approximately 0.0000258 or 0.00258%.