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
If a person buys one LOTTO ticket, what is his probability of winning the grand price?
Number of ways to draw 6 numbers from 20
is C(20,6)
= 20!/(6!14!)
= 38760
so prob(winner) = 1/38760
If a person buys 1000 LOTTO tickets, what is his probability of winning the grand prize?
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
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%.